Theorem anbi1cd 33997

Description: Introduce a left and the same right conjunct to the sides of a logical equivalence, deduction form. (Contributed by Peter Mazsa, 22-May-2021.)

Hypothesis

Ref	Expression
anbi1cd.1	|- ( ph -> ( ps <-> ch ) )

Assertion

Ref	Expression
anbi1cd	|- ( ph -> ( ( th /\ ps ) <-> ( ch /\ th ) ) )

Proof of Theorem anbi1cd

Step	Hyp	Ref	Expression
1		anbi1cd.1	. 2 |- ( ph -> ( ps <-> ch ) )
2		anbi2 744	. . 3 |- ( ( ps <-> ch ) -> ( ( th /\ ps ) <-> ( th /\ ch ) ) )
3	2	biancomd 33995	. 2 |- ( ( ps <-> ch ) -> ( ( th /\ ps ) <-> ( ch /\ th ) ) )
4	1, 3	syl 17	1 |- ( ph -> ( ( th /\ ps ) <-> ( ch /\ th ) ) )

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:  opelresALTV  34031  eccnvepres  34045