Theorem tbt 541

Description: A wff is equivalent to its equivalence with truth.

Hypothesis

Ref	Expression
tbt.1	|- ph

Assertion

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

Proof of Theorem tbt

Step	Hyp	Ref	Expression
1		tbt.1	. . . . 5 |- ph
2	1	a1i 7	. . . 4 |- (ps -> ph)
3	2	a1d 14	. . 3 |- (ps -> (ps -> ph))
4		ax-1 3	. . 3 |- (ps -> (ph -> ps))
5	3, 4	impbid 397	. 2 |- (ps -> (ps <-> ph))
6		bi2 131	. . 3 |- ((ps <-> ph) -> (ph -> ps))
7	1, 6	mpi 44	. 2 |- ((ps <-> ph) -> ps)
8	5, 7	impbi 139	1 |- (ps <-> (ps <-> ph))

Syntax hints:   <-> wb 127

This theorem is referenced by:  exists1 1072  nvelv 1483

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

This theorem depends on definitions:  df-bi 128  df-an 198

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