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  2778  rexcom4b  2797  eueq  2944  ssrabeq  3280  a9evsep  4167  pwunim  4334  elvv  4738  elvvv  4739  resopab  5004  funfn  5302  dffn2  5429  dffn3  5438  dffn4  5506  fsn  5754  ixp0x  6815  ac6sfi  6997  fimax2gtri  7000  nninfwlporlemd  7276  xrmaxiflemcom  11593  plyun0  15241  trirec0xor  16021