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Mirrors > Home > ILE Home > Th. List > pm5.32 | Unicode version |
Description: Distribution of implication over biconditional. Theorem *5.32 of [WhiteheadRussell] p. 125. (Contributed by NM, 1-Aug-1994.) (Revised by NM, 31-Jan-2015.) |
Ref | Expression |
---|---|
pm5.32 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . . 3 | |
2 | 1 | pm5.32d 447 | . 2 |
3 | ibar 299 | . . . 4 | |
4 | ibar 299 | . . . 4 | |
5 | 3, 4 | bibi12d 234 | . . 3 |
6 | 5 | biimprcd 159 | . 2 |
7 | 2, 6 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: pm5.32i 451 biadani 607 xordidc 1394 cbvex2 1915 rabbi 2647 rabxfrd 4452 asymref 4994 rexrnmpt 5637 mpo2eqb 5960 |
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