Theorem anbi1 687

Description: Introduce a right conjunct to both sides of a logical equivalence. Theorem *4.36 of [WhiteheadRussell] p. 118. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
anbi1	|- ((ph <-> ps) -> ((ph /\ ch) <-> (ps /\ ch)))

Proof of Theorem anbi1

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ((ph <-> ps) -> (ph <-> ps))
2	1	anbi1d 685	1 |- ((ph <-> ps) -> ((ph /\ ch) <-> (ps /\ ch)))

Syntax hints:   -> wi 4   <-> wb 176   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  pm5.75  903  nanbi1  1295