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  943  isset  2766  rexcom4b  2785  eueq  2931  ssrabeq  3266  a9evsep  4151  pwunim  4317  elvv  4721  elvvv  4722  resopab  4986  funfn  5284  dffn2  5405  dffn3  5414  dffn4  5482  fsn  5730  ixp0x  6780  ac6sfi  6954  fimax2gtri  6957  nninfwlporlemd  7231  xrmaxiflemcom  11392  plyun0  14882  trirec0xor  15535