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Theorem pm4.71 611
Description: Implication in terms of biconditional and conjunction. Theorem *4.71 of [WhiteheadRussell] p. 120. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 2-Dec-2012.)
Assertion
Ref Expression
pm4.71

Proof of Theorem pm4.71
StepHypRef Expression
1 simpl 443 . . 3
21biantru 491 . 2
3 anclb 530 . 2
4 dfbi2 609 . 2
52, 3, 43bitr4i 268 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   wa 358
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 177  df-an 360
This theorem is referenced by:  pm4.71r  612  pm4.71i  613  pm4.71d  615  bigolden  901  pm5.75  903  exintrbi  1613  rabid2  2788  dfss2  3262  disj3  3595  dmopab3  4917  resopab2  5001  resoprab2  5582
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