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Mirrors > Home > ILE Home > Th. List > pm5.32d | Unicode version |
Description: Distribution of implication over biconditional (deduction form). (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 | biimp 117 | . . . 4 | |
3 | 1, 2 | syl6 33 | . . 3 |
4 | 3 | imdistand 444 | . 2 |
5 | biimpr 129 | . . . 4 | |
6 | 1, 5 | syl6 33 | . . 3 |
7 | 6 | imdistand 444 | . 2 |
8 | 4, 7 | impbid 128 | 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: pm5.32rd 447 pm5.32da 448 pm5.32 449 anbi2d 460 cbvex2 1902 cores 5089 isoini 5768 mpoeq123 5880 genpassl 7444 genpassu 7445 fzind 9279 btwnz 9283 elfzm11 9993 isprm2 11993 isprm3 11994 |
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