Theorem mpbiran2 847

Description: Detach truth from conjunction in biconditional. (Contributed by NM, 22-Feb-1996.) (Revised by NM, 9-Jan-2015.)

Hypotheses

Ref	Expression
mpbiran2.1	|- ch
mpbiran2.2	|- (ph <-> (ps /\ ch))

Assertion

Ref	Expression
mpbiran2	|- (ph <-> ps)

Proof of Theorem mpbiran2

Step	Hyp	Ref	Expression
1		mpbiran2.2	. 2 |- (ph <-> (ps /\ ch))
2		mpbiran2.1	. . 3 |- ch
3	2	biantru 286	. 2 |- (ps <-> (ps /\ ch))
4	1, 3	bitr4i 176	1 |- (ph <-> ps)

Syntax hints:   /\ wa 97   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  reueq  2732  ss0b  3250  eusv1  4150  eusv2nf  4154  eusv2  4155  opthprc  4334  opelres  4560  f1cnvcnv  5043  fores  5058  f1orn  5079  funfvdm  5179  dfoprab2  5494  tpostpos  5820  opelreal  6726  elreal2  6728  eqresr  6733  axprecex  6764  bdeq0  9322