Theorem tbt 359

Description: A wff is equivalent to its equivalence with a 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 358	. . 3 |- ( ( ph -> ps ) <-> ( ph -> ( ps <-> ph ) ) )
3	2	pm5.74ri 261	. 2 |- ( ph -> ( ps <-> ( ps <-> ph ) ) )
4	1, 3	ax-mp 5	1 |- ( ps <-> ( ps <-> ph ) )

Syntax hints:   <-> wb 196

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

This theorem depends on definitions:  df-bi 197

This theorem is referenced by:  tbtru  1494  exists1  2561  eqvf  3204  reu6  3395  vprc  4796  iotanul  5866  elnev  38639