Theorem tbt 720

Description: A wff is equivalent to its equivalence with truth. (The proof was shortened by Juha Arpiainen, 19-Jan-2006.)

Hypothesis

Ref	Expression
tbt.1	|- ph

Assertion

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

Proof of Theorem tbt

Step	Hyp	Ref	Expression
1		tbt.1	. . 3 |- ph
2		pm5.501 595	. . 3 |- (ph -> (ps <-> (ph <-> ps)))
3	1, 2	ax-mp 7	. 2 |- (ps <-> (ph <-> ps))
4		bicom 520	. 2 |- ((ph <-> ps) <-> (ps <-> ph))
5	3, 4	bitr 173	1 |- (ps <-> (ps <-> ph))

Syntax hints:   <-> wb 146

This theorem is referenced by:  exists1 1457  reu3 1931  eqv 2295  nvelv 2713  asymref2 3440

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 147  df-an 225

Copyright terms: Public domain