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  950  isset  2819  rexcom4b  2838  eueq  2987  ssrabeq  3325  a9evsep  4231  pwunim  4406  elvv  4811  elvvv  4812  resopab  5081  funfn  5381  dffn2  5509  dffn3  5518  dffn4  5595  fsn  5848  ixp0x  6960  ac6sfi  7154  fimax2gtri  7158  nninfwlporlemd  7462  ccatrcan  11404  xrmaxiflemcom  11927  plyun0  15588  trirec0xor  16816