Theorem anbi2 744

Description: Introduce a left conjunct to both sides of a logical equivalence. (Contributed by NM, 16-Nov-2013.)

Assertion

Ref	Expression
anbi2	|- ( ( ph <-> ps ) -> ( ( ch /\ ph ) <-> ( ch /\ ps ) ) )

Proof of Theorem anbi2

Step	Hyp	Ref	Expression
1		id 22	. 2 |- ( ( ph <-> ps ) -> ( ph <-> ps ) )
2	1	anbi2d 740	1 |- ( ( ph <-> ps ) -> ( ( ch /\ ph ) <-> ( ch /\ ps ) ) )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384

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 197  df-an 386

This theorem is referenced by:  eleq2d  2687  anbi1cd  33997