Theorem ancrb 330

Description: Conjoin antecedent to right of consequent.

Assertion

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

Proof of Theorem ancrb

Step	Hyp	Ref	Expression
1		ancr 295	. 2 |- ((ph -> ps) -> (ph -> (ps /\ ph)))
2		pm3.26 319	. . 3 |- ((ps /\ ph) -> ps)
3	2	imim2i 17	. 2 |- ((ph -> (ps /\ ph)) -> (ph -> ps))
4	1, 3	impbi 157	1 |- ((ph -> ps) <-> (ph -> (ps /\ ph)))

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

This theorem is referenced by:  iba 642

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