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Theorem pm5.74 244
Description: Distribution of implication over biconditional. Theorem *5.74 of [WhiteheadRussell] p. 126. (Contributed by NM, 1-Aug-1994.) (Proof shortened by Wolf Lammen, 11-Apr-2013.)
Assertion
Ref Expression
pm5.74

Proof of Theorem pm5.74
StepHypRef Expression
1 bi1 186 . . . 4
21imim3i 59 . . 3
3 bi2 198 . . . 4
43imim3i 59 . . 3
52, 4impbid 191 . 2
6 bi1 186 . . . 4
76pm2.86d 99 . . 3
8 bi2 198 . . . 4
98pm2.86d 99 . . 3
107, 9impbidd 189 . 2
115, 10impbii 188 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184
This theorem is referenced by:  pm5.74i  245  pm5.74ri  246  pm5.74d  247  pm5.74rd  248  bibi2d  318  pm5.32  636  orbidi  932
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185
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