Theorem anbi1cd 465

Description: Introduce a proposition as left conjunct on the left-hand side and right conjunct on the right-hand side of an 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	. . 3 |- ( ph -> ( ps <-> ch ) )
2	1	anbi2d 461	. 2 |- ( ph -> ( ( th /\ ps ) <-> ( th /\ ch ) ) )
3	2	biancomd 269	1 |- ( ph -> ( ( th /\ ps ) <-> ( ch /\ th ) ) )

Syntax hints:   -> wi 4   /\ wa 103   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)