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Mirrors > Home > ILE Home > Th. List > pm5.32d | Unicode version |
Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 29-Oct-1996.) (Revised by NM, 31-Jan-2015.) |
Ref | Expression |
---|---|
pm5.32d.1 |
Ref | Expression |
---|---|
pm5.32d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.32d.1 | . . . 4 | |
2 | bi1 111 | . . . 4 | |
3 | 1, 2 | syl6 29 | . . 3 |
4 | 3 | imdistand 421 | . 2 |
5 | bi2 121 | . . . 4 | |
6 | 1, 5 | syl6 29 | . . 3 |
7 | 6 | imdistand 421 | . 2 |
8 | 4, 7 | impbid 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: pm5.32rd 424 pm5.32da 425 pm5.32 426 anbi2d 437 cbvex2 1797 cores 4824 isoini 5457 mpt2eq123 5564 genpassl 6622 genpassu 6623 fzind 8353 btwnz 8357 elfzm11 8953 |
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