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Theorem List for Intuitionistic Logic Explorer - 7801-7900   *Has distinct variable group(s)
TypeLabelDescription
Statement

Theorem2p1e3 7801 2 + 1 = 3. (Contributed by Mario Carneiro, 18-Apr-2015.)
(2 + 1) = 3

Theorem1p2e3 7802 1 + 2 = 3 (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)
(1 + 2) = 3

Theorem3p1e4 7803 3 + 1 = 4. (Contributed by Mario Carneiro, 18-Apr-2015.)
(3 + 1) = 4

Theorem4p1e5 7804 4 + 1 = 5. (Contributed by Mario Carneiro, 18-Apr-2015.)
(4 + 1) = 5

Theorem5p1e6 7805 5 + 1 = 6. (Contributed by Mario Carneiro, 18-Apr-2015.)
(5 + 1) = 6

Theorem6p1e7 7806 6 + 1 = 7. (Contributed by Mario Carneiro, 18-Apr-2015.)
(6 + 1) = 7

Theorem7p1e8 7807 7 + 1 = 8. (Contributed by Mario Carneiro, 18-Apr-2015.)
(7 + 1) = 8

Theorem8p1e9 7808 8 + 1 = 9. (Contributed by Mario Carneiro, 18-Apr-2015.)
(8 + 1) = 9

Theorem9p1e10 7809 9 + 1 = 10. (Contributed by Mario Carneiro, 18-Apr-2015.)
(9 + 1) = 10

Theorem3p2e5 7810 3 + 2 = 5. (Contributed by NM, 11-May-2004.)
(3 + 2) = 5

Theorem3p3e6 7811 3 + 3 = 6. (Contributed by NM, 11-May-2004.)
(3 + 3) = 6

Theorem4p2e6 7812 4 + 2 = 6. (Contributed by NM, 11-May-2004.)
(4 + 2) = 6

Theorem4p3e7 7813 4 + 3 = 7. (Contributed by NM, 11-May-2004.)
(4 + 3) = 7

Theorem4p4e8 7814 4 + 4 = 8. (Contributed by NM, 11-May-2004.)
(4 + 4) = 8

Theorem5p2e7 7815 5 + 2 = 7. (Contributed by NM, 11-May-2004.)
(5 + 2) = 7

Theorem5p3e8 7816 5 + 3 = 8. (Contributed by NM, 11-May-2004.)
(5 + 3) = 8

Theorem5p4e9 7817 5 + 4 = 9. (Contributed by NM, 11-May-2004.)
(5 + 4) = 9

Theorem5p5e10 7818 5 + 5 = 10. (Contributed by NM, 5-Feb-2007.)
(5 + 5) = 10

Theorem6p2e8 7819 6 + 2 = 8. (Contributed by NM, 11-May-2004.)
(6 + 2) = 8

Theorem6p3e9 7820 6 + 3 = 9. (Contributed by NM, 11-May-2004.)
(6 + 3) = 9

Theorem6p4e10 7821 6 + 4 = 10. (Contributed by NM, 5-Feb-2007.)
(6 + 4) = 10

Theorem7p2e9 7822 7 + 2 = 9. (Contributed by NM, 11-May-2004.)
(7 + 2) = 9

Theorem7p3e10 7823 7 + 3 = 10. (Contributed by NM, 5-Feb-2007.)
(7 + 3) = 10

Theorem8p2e10 7824 8 + 2 = 10. (Contributed by NM, 5-Feb-2007.)
(8 + 2) = 10

Theorem1t1e1 7825 1 times 1 equals 1. (Contributed by David A. Wheeler, 7-Jul-2016.)
(1 · 1) = 1

Theorem2t1e2 7826 2 times 1 equals 2. (Contributed by David A. Wheeler, 6-Dec-2018.)
(2 · 1) = 2

Theorem2t2e4 7827 2 times 2 equals 4. (Contributed by NM, 1-Aug-1999.)
(2 · 2) = 4

Theorem3t1e3 7828 3 times 1 equals 3. (Contributed by David A. Wheeler, 8-Dec-2018.)
(3 · 1) = 3

Theorem3t2e6 7829 3 times 2 equals 6. (Contributed by NM, 2-Aug-2004.)
(3 · 2) = 6

Theorem3t3e9 7830 3 times 3 equals 9. (Contributed by NM, 11-May-2004.)
(3 · 3) = 9

Theorem4t2e8 7831 4 times 2 equals 8. (Contributed by NM, 2-Aug-2004.)
(4 · 2) = 8

Theorem5t2e10 7832 5 times 2 equals 10. (Contributed by NM, 5-Feb-2007.)
(5 · 2) = 10

Theorem2t0e0 7833 2 times 0 equals 0. (Contributed by David A. Wheeler, 8-Dec-2018.)
(2 · 0) = 0

Theorem4d2e2 7834 One half of four is two. (Contributed by NM, 3-Sep-1999.)
(4 / 2) = 2

Theorem2nn 7835 2 is a positive integer. (Contributed by NM, 20-Aug-2001.)
2

Theorem3nn 7836 3 is a positive integer. (Contributed by NM, 8-Jan-2006.)
3

Theorem4nn 7837 4 is a positive integer. (Contributed by NM, 8-Jan-2006.)
4

Theorem5nn 7838 5 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013.)
5

Theorem6nn 7839 6 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013.)
6

Theorem7nn 7840 7 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013.)
7

Theorem8nn 7841 8 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013.)
8

Theorem9nn 7842 9 is a positive integer. (Contributed by NM, 21-Oct-2012.)
9

Theorem10nn 7843 10 is a positive integer. (Contributed by NM, 8-Nov-2012.)
10

Theorem1lt2 7844 1 is less than 2. (Contributed by NM, 24-Feb-2005.)
1 < 2

Theorem2lt3 7845 2 is less than 3. (Contributed by NM, 26-Sep-2010.)
2 < 3

Theorem1lt3 7846 1 is less than 3. (Contributed by NM, 26-Sep-2010.)
1 < 3

Theorem3lt4 7847 3 is less than 4. (Contributed by Mario Carneiro, 15-Sep-2013.)
3 < 4

Theorem2lt4 7848 2 is less than 4. (Contributed by Mario Carneiro, 15-Sep-2013.)
2 < 4

Theorem1lt4 7849 1 is less than 4. (Contributed by Mario Carneiro, 15-Sep-2013.)
1 < 4

Theorem4lt5 7850 4 is less than 5. (Contributed by Mario Carneiro, 15-Sep-2013.)
4 < 5

Theorem3lt5 7851 3 is less than 5. (Contributed by Mario Carneiro, 15-Sep-2013.)
3 < 5

Theorem2lt5 7852 2 is less than 5. (Contributed by Mario Carneiro, 15-Sep-2013.)
2 < 5

Theorem1lt5 7853 1 is less than 5. (Contributed by Mario Carneiro, 15-Sep-2013.)
1 < 5

Theorem5lt6 7854 5 is less than 6. (Contributed by Mario Carneiro, 15-Sep-2013.)
5 < 6

Theorem4lt6 7855 4 is less than 6. (Contributed by Mario Carneiro, 15-Sep-2013.)
4 < 6

Theorem3lt6 7856 3 is less than 6. (Contributed by Mario Carneiro, 15-Sep-2013.)
3 < 6

Theorem2lt6 7857 2 is less than 6. (Contributed by Mario Carneiro, 15-Sep-2013.)
2 < 6

Theorem1lt6 7858 1 is less than 6. (Contributed by NM, 19-Oct-2012.)
1 < 6

Theorem6lt7 7859 6 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013.)
6 < 7

Theorem5lt7 7860 5 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013.)
5 < 7

Theorem4lt7 7861 4 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013.)
4 < 7

Theorem3lt7 7862 3 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013.)
3 < 7

Theorem2lt7 7863 2 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013.)
2 < 7

Theorem1lt7 7864 1 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013.)
1 < 7

Theorem7lt8 7865 7 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013.)
7 < 8

Theorem6lt8 7866 6 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013.)
6 < 8

Theorem5lt8 7867 5 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013.)
5 < 8

Theorem4lt8 7868 4 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013.)
4 < 8

Theorem3lt8 7869 3 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013.)
3 < 8

Theorem2lt8 7870 2 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013.)
2 < 8

Theorem1lt8 7871 1 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013.)
1 < 8

Theorem8lt9 7872 8 is less than 9. (Contributed by Mario Carneiro, 19-Feb-2014.)
8 < 9

Theorem7lt9 7873 7 is less than 9. (Contributed by Mario Carneiro, 9-Mar-2015.)
7 < 9

Theorem6lt9 7874 6 is less than 9. (Contributed by Mario Carneiro, 9-Mar-2015.)
6 < 9

Theorem5lt9 7875 5 is less than 9. (Contributed by Mario Carneiro, 9-Mar-2015.)
5 < 9

Theorem4lt9 7876 4 is less than 9. (Contributed by Mario Carneiro, 9-Mar-2015.)
4 < 9

Theorem3lt9 7877 3 is less than 9. (Contributed by Mario Carneiro, 9-Mar-2015.)
3 < 9

Theorem2lt9 7878 2 is less than 9. (Contributed by Mario Carneiro, 9-Mar-2015.)
2 < 9

Theorem1lt9 7879 1 is less than 9. (Contributed by NM, 19-Oct-2012.) (Revised by Mario Carneiro, 9-Mar-2015.)
1 < 9

Theorem9lt10 7880 9 is less than 10. (Contributed by Mario Carneiro, 8-Feb-2015.)
9 < 10

Theorem8lt10 7881 8 is less than 10. (Contributed by Mario Carneiro, 8-Feb-2015.)
8 < 10

Theorem7lt10 7882 7 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015.)
7 < 10

Theorem6lt10 7883 6 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015.)
6 < 10

Theorem5lt10 7884 5 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015.)
5 < 10

Theorem4lt10 7885 4 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015.)
4 < 10

Theorem3lt10 7886 3 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015.)
3 < 10

Theorem2lt10 7887 2 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015.)
2 < 10

Theorem1lt10 7888 1 is less than 10. (Contributed by NM, 7-Nov-2012.) (Revised by Mario Carneiro, 9-Mar-2015.)
1 < 10

Theorem0ne2 7889 0 is not equal to 2. (Contributed by David A. Wheeler, 8-Dec-2018.)
0 ≠ 2

Theorem1ne2 7890 1 is not equal to 2. (Contributed by NM, 19-Oct-2012.)
1 ≠ 2

Theorem1le2 7891 1 is less than or equal to 2 (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)
1 ≤ 2

Theorem2cnne0 7892 2 is a nonzero complex number (common case). (Contributed by David A. Wheeler, 7-Dec-2018.)
(2 2 ≠ 0)

Theorem2rene0 7893 2 is a nonzero real number (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)
(2 2 ≠ 0)

Theorem1le3 7894 1 is less than or equal to 3. (Contributed by David A. Wheeler, 8-Dec-2018.)
1 ≤ 3

Theoremneg1mulneg1e1 7895 -1 · -1 is 1 (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)
(-1 · -1) = 1

Theoremhalfre 7896 One-half is real. (Contributed by David A. Wheeler, 8-Dec-2018.)
(1 / 2)

Theoremhalfcn 7897 One-half is complex. (Contributed by David A. Wheeler, 8-Dec-2018.)
(1 / 2)

Theoremhalfgt0 7898 One-half is greater than zero. (Contributed by NM, 24-Feb-2005.)
0 < (1 / 2)

Theoremhalflt1 7899 One-half is less than one. (Contributed by NM, 24-Feb-2005.)
(1 / 2) < 1

Theorem1mhlfehlf 7900 Prove that 1 - 1/2 = 1/2. (Contributed by David A. Wheeler, 4-Jan-2017.)
(1 − (1 / 2)) = (1 / 2)

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