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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 | bi1 117 |
. . . 4
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3 | 1, 2 | syl6 33 |
. . 3
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4 | 3 | imdistand 444 |
. 2
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5 | bi2 129 |
. . . 4
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6 | 1, 5 | syl6 33 |
. . 3
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7 | 6 | imdistand 444 |
. 2
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8 | 4, 7 | impbid 128 |
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 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 1895 cores 5050 isoini 5727 mpoeq123 5838 genpassl 7356 genpassu 7357 fzind 9190 btwnz 9194 elfzm11 9902 isprm2 11834 isprm3 11835 |
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