Theorem biantru 302

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 300	. 2 |- ( ph -> ( ps <-> ( ps /\ ph ) ) )
3	1, 2	ax-mp 5	1 |- ( ps <-> ( ps /\ ph ) )

Syntax hints:   /\ wa 104   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm4.71  389  mpbiran2  949  isset  2808  rexcom4b  2827  eueq  2976  ssrabeq  3313  a9evsep  4212  pwunim  4385  elvv  4790  elvvv  4791  resopab  5059  funfn  5358  dffn2  5486  dffn3  5495  dffn4  5568  fsn  5822  ixp0x  6900  ac6sfi  7092  fimax2gtri  7096  nninfwlporlemd  7376  ccatrcan  11309  xrmaxiflemcom  11832  plyun0  15489  trirec0xor  16716