Theorem biantru 286

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 284	. 2 |- (ph -> (ps <-> (ps /\ ph)))
3	1, 2	ax-mp 7	1 |- (ps <-> (ps /\ ph))

Syntax hints:   /\ wa 97   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  pm4.71  369  mpbiran2  847  isset  2555  rexcom4b  2573  eueq  2706  ssrabeq  3020  nsspssun  3164  disjpss  3272  a9evsep  3870  pwunim  4014  elvv  4345  elvvv  4346  resopab  4595  funfn  4874  dffn2  4990  dffn3  4996  dffn4  5055  fsn  5278