Theorem biantru 296

Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
biantru.1	|- ph

Assertion

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

Proof of Theorem biantru

Step	Hyp	Ref	Expression
1		biantru.1	. 2 |- ph
2		iba 294	. 2 |- ( ph -> ( ps <-> ( ps /\ ph ) ) )
3	1, 2	ax-mp 7	1 |- ( ps <-> ( ps /\ ph ) )

Syntax hints:   /\ 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:  pm4.71  381  mpbiran2  883  isset  2606  rexcom4b  2625  eueq  2764  ssrabeq  3081  a9evsep  3908  pwunim  4049  elvv  4428  elvvv  4429  resopab  4682  funfn  4961  dffn2  5078  dffn3  5084  dffn4  5143  fsn  5367  ac6sfi  6431