Theorem a1bi 172

Description: Inference rule introducing a theorem as an antecedent.

Hypothesis

Ref	Expression
a1bi.1	|- ph

Assertion

Ref	Expression
a1bi	|- (ps <-> (ph -> ps))

Proof of Theorem a1bi

Step	Hyp	Ref	Expression
1		ax-1 3	. 2 |- (ps -> (ph -> ps))
2		a1bi.1	. . 3 |- ph
3		pm2.27 30	. . 3 |- (ph -> ((ph -> ps) -> ps))
4	2, 3	ax-mp 6	. 2 |- ((ph -> ps) -> ps)
5	1, 4	impbi 139	1 |- (ps <-> (ph -> ps))

Syntax hints:   -> wi 2   <-> wb 127

This theorem is referenced by:  sbequ8 902  ralv 1357  hbsbcv 1447  pw2en 3348

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

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