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Mirrors > Home > ILE Home > Th. List > pm5.21 | Unicode version |
Description: Two propositions are equivalent if they are both false. Theorem *5.21 of [WhiteheadRussell] p. 124. (Contributed by NM, 21-May-1994.) (Revised by Mario Carneiro, 31-Jan-2015.) |
Ref | Expression |
---|---|
pm5.21 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 107 | . . 3 | |
2 | 1 | pm2.21d 581 | . 2 |
3 | simpr 108 | . . 3 | |
4 | 3 | pm2.21d 581 | . 2 |
5 | 2, 4 | impbid 127 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 wb 103 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in2 577 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: pm5.21im 644 |
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