Theorem tbt 333

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 332	. . 3 |- ((ph -> ps) <-> (ph -> (ps <-> ph)))
3	2	pm5.74ri 237	. 2 |- (ph -> (ps <-> (ps <-> ph)))
4	1, 3	ax-mp 8	1 |- (ps <-> (ps <-> ph))

Syntax hints:   <-> wb 176

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  tbtru  1324  exists1  2293  reu6  3025  eqv  3565