Theorem bianabs 575

Description: Absorb a hypothesis into the second member of a biconditional. (Contributed by FL, 15-Feb-2007.)

Hypothesis

Ref	Expression
bianabs.1	|- ( ph -> ( ps <-> ( ph /\ ch ) ) )

Assertion

Ref	Expression
bianabs	|- ( ph -> ( ps <-> ch ) )

Proof of Theorem bianabs

Step	Hyp	Ref	Expression
1		bianabs.1	. 2 |- ( ph -> ( ps <-> ( ph /\ ch ) ) )
2		ibar 295	. 2 |- ( ph -> ( ch <-> ( ph /\ ch ) ) )
3	1, 2	bitr4d 189	1 |- ( ph -> ( ps <-> ch ) )

Syntax hints:   -> wi 4   /\ wa 102   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  ceqsrexv  2725  opelopab2a  4020  ov  5640  ovg  5659  ltresr  7007