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Mirrors > Home > ILE Home > Th. List > xoranor | Unicode version |
Description: One way of defining exclusive or. Equivalent to df-xor 1267. (Contributed by Jim Kingdon and Mario Carneiro, 1-Mar-2018.) |
Ref | Expression |
---|---|
xoranor |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xor 1267 | . . 3 | |
2 | ax-ia3 101 | . . . . . . 7 | |
3 | 2 | con3d 561 | . . . . . 6 |
4 | olc 632 | . . . . . 6 | |
5 | 3, 4 | syl6 29 | . . . . 5 |
6 | pm3.21 251 | . . . . . . 7 | |
7 | 6 | con3d 561 | . . . . . 6 |
8 | orc 633 | . . . . . 6 | |
9 | 7, 8 | syl6 29 | . . . . 5 |
10 | 5, 9 | jaoi 636 | . . . 4 |
11 | 10 | imdistani 419 | . . 3 |
12 | 1, 11 | sylbi 114 | . 2 |
13 | pm3.14 670 | . . . 4 | |
14 | 13 | anim2i 324 | . . 3 |
15 | 14, 1 | sylibr 137 | . 2 |
16 | 12, 15 | impbii 117 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wb 98 wo 629 wxo 1266 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 |
This theorem depends on definitions: df-bi 110 df-xor 1267 |
This theorem is referenced by: excxor 1269 xoror 1270 |
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