Theorem anclb 329

Description: Conjoin antecedent to left of consequent. Theorem *4.7 of [WhiteheadRussell] p. 120.

Assertion

Ref	Expression
anclb	|- ((ph -> ps) <-> (ph -> (ph /\ ps)))

Proof of Theorem anclb

Step	Hyp	Ref	Expression
1		ancl 294	. 2 |- ((ph -> ps) -> (ph -> (ph /\ ps)))
2		pm3.27 323	. . 3 |- ((ph /\ ps) -> ps)
3	2	imim2i 17	. 2 |- ((ph -> (ph /\ ps)) -> (ph -> ps))
4	1, 3	impbi 157	1 |- ((ph -> ps) <-> (ph -> (ph /\ ps)))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223

This theorem is referenced by:  ibar 645  dfpss3 2137

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 147  df-an 225

Copyright terms: Public domain