Theorem tbt 785

Description: A wff is equivalent to its equivalence with truth. (The proof was 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 648	. . 3 |- ((ph -> ps) <-> (ph -> (ps <-> ph)))
3	2	pm5.74ri 644	. 2 |- (ph -> (ps <-> (ps <-> ph)))
4	1, 3	ax-mp 7	1 |- (ps <-> (ps <-> ph))

Syntax hints:   <-> wb 162

This theorem is referenced by:  exists1 1699  reu6 2276  eqv 2719  vprc 3264  asymref2OLD 4122  truvar 13832  elnev 16086

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 163  df-an 241

Copyright terms: Public domain