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  2932  ssrabeq  3267  a9evsep  4152  pwunim  4318  elvv  4722  elvvv  4723  resopab  4987  funfn  5285  dffn2  5406  dffn3  5415  dffn4  5483  fsn  5731  ixp0x  6782  ac6sfi  6956  fimax2gtri  6959  nninfwlporlemd  7233  xrmaxiflemcom  11395  plyun0  14915  trirec0xor  15605