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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 |
. . 3
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2 | 1 | pm5.32d 446 |
. 2
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3 | ibar 299 |
. . . 4
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4 | ibar 299 |
. . . 4
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5 | 3, 4 | bibi12d 234 |
. . 3
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6 | 5 | biimprcd 159 |
. 2
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7 | 2, 6 | impbii 125 |
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: pm5.32i 450 biadani 602 xordidc 1378 cbvex2 1895 rabbi 2611 rabxfrd 4398 asymref 4932 rexrnmpt 5571 mpo2eqb 5888 |
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