Theorem ancrb 265

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 243	. 2 |- ((ph -> ps) -> (ph -> (ps /\ ph)))
2		pm3.26 256	. . 3 |- ((ps /\ ph) -> ps)
3	2	syl3 18	. 2 |- ((ph -> (ps /\ ph)) -> (ph -> ps))
4	1, 3	impbi 139	1 |- ((ph -> ps) <-> (ph -> (ps /\ ph)))

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

This theorem is referenced by:  iba 486

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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