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  944  isset  2784  rexcom4b  2803  eueq  2952  ssrabeq  3289  a9evsep  4183  pwunim  4352  elvv  4756  elvvv  4757  resopab  5023  funfn  5321  dffn2  5448  dffn3  5457  dffn4  5527  fsn  5777  ixp0x  6838  ac6sfi  7023  fimax2gtri  7026  nninfwlporlemd  7302  ccatrcan  11212  xrmaxiflemcom  11721  plyun0  15369  trirec0xor  16294