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Mirrors > Home > ILE Home > Th. List > annimim | Unicode version |
Description: Express conjunction in terms of implication. One direction of Theorem *4.61 of [WhiteheadRussell] p. 120. The converse holds for decidable propositions, as can be seen at annimdc 845. (Contributed by Jim Kingdon, 24-Dec-2017.) |
Ref | Expression |
---|---|
annimim |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.27 35 | . . 3 | |
2 | con3 571 | . . 3 | |
3 | 1, 2 | syl 14 | . 2 |
4 | 3 | imp 115 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-in1 544 ax-in2 545 |
This theorem is referenced by: pm4.65r 783 dcim 784 imanim 785 pm4.52im 803 exanaliim 1538 |
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