Theorem tbt 245

Description: A wff is equivalent to its equivalence with truth. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Hypothesis

Ref	Expression
tbt.1	|- ph

Assertion

Ref	Expression
tbt	|- ( ps <-> ( ps <-> ph ) )

Proof of Theorem tbt

Step	Hyp	Ref	Expression
1		tbt.1	. 2 |- ph
2		ibibr 244	. . 3 |- ( ( ph -> ps ) <-> ( ph -> ( ps <-> ph ) ) )
3	2	pm5.74ri 179	. 2 |- ( ph -> ( ps <-> ( ps <-> ph ) ) )
4	1, 3	ax-mp 7	1 |- ( ps <-> ( ps <-> ph ) )

Syntax hints:   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  tbtru  1299  exists1  2044  reu6  2804  eqv  3302  vnex  3970  bj-vprc  11787