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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 |
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Ref | Expression |
---|---|
pm5.32d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.32d.1 |
. . . 4
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2 | biimp 118 |
. . . 4
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3 | 1, 2 | syl6 33 |
. . 3
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4 | 3 | imdistand 447 |
. 2
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5 | biimpr 130 |
. . . 4
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6 | 1, 5 | syl6 33 |
. . 3
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7 | 6 | imdistand 447 |
. 2
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8 | 4, 7 | impbid 129 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: pm5.32rd 451 pm5.32da 452 pm5.32 453 anbi2d 464 cbvex2 1922 cores 5134 isoini 5821 mpoeq123 5936 genpassl 7525 genpassu 7526 fzind 9370 btwnz 9374 elfzm11 10093 isprm2 12119 isprm3 12120 modprminv 12251 modprminveq 12252 |
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