Theorem pm4.45im 359

Description: Conjunction with implication. Compare Theorem *4.45 of [WhiteheadRussell] p. 119.

Assertion

Ref	Expression
pm4.45im	|- (ph <-> (ph /\ (ps -> ph)))

Proof of Theorem pm4.45im

Step	Hyp	Ref	Expression
1		ax-1 4	. . 3 |- (ph -> (ps -> ph))
2	1	ancli 320	. 2 |- (ph -> (ph /\ (ps -> ph)))
3		simpl 346	. 2 |- ((ph /\ (ps -> ph)) -> ph)
4	2, 3	impbii 174	1 |- (ph <-> (ph /\ (ps -> ph)))

Syntax hints:   -> wi 3   <-> wb 163   /\ wa 240

This theorem is referenced by:  difdif 2734

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242

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