Theorem pm4.71r 482

Description: Implication in terms of biconditional and conjunction. Theorem *4.71 of [WhiteheadRussell] p. 120 (with conjunct reversed).

Assertion

Ref	Expression
pm4.71r	|- ((ph -> ps) <-> (ph <-> (ps /\ ph)))

Proof of Theorem pm4.71r

Step	Hyp	Ref	Expression
1		pm4.71 481	. 2 |- ((ph -> ps) <-> (ph <-> (ph /\ ps)))
2		ancom 333	. . 3 |- ((ph /\ ps) <-> (ps /\ ph))
3	2	bibi2i 460	. 2 |- ((ph <-> (ph /\ ps)) <-> (ph <-> (ps /\ ph)))
4	1, 3	bitr 151	1 |- ((ph -> ps) <-> (ph <-> (ps /\ ph)))

Syntax hints:   -> wi 2   <-> wb 127   /\ wa 196

This theorem is referenced by:  pm4.71ri 484  bimsc1 557  reuhyp 1581  ordsucun 2333  iss 2599  fcoi1 2765  feu 2767  fnopabfv 2858  fniunfv 2860  shselt 5280

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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