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  947  isset  2806  rexcom4b  2825  eueq  2974  ssrabeq  3311  a9evsep  4206  pwunim  4378  elvv  4783  elvvv  4784  resopab  5052  funfn  5351  dffn2  5478  dffn3  5487  dffn4  5559  fsn  5812  ixp0x  6886  ac6sfi  7073  fimax2gtri  7077  nninfwlporlemd  7355  ccatrcan  11272  xrmaxiflemcom  11781  plyun0  15431  trirec0xor  16527