Theorem a1bi 327

Description: Inference rule introducing a theorem as an antecedent. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 11-Nov-2012.)

Hypothesis

Ref	Expression
a1bi.1	|- ph

Assertion

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

Proof of Theorem a1bi

Step	Hyp	Ref	Expression
1		a1bi.1	. 2 |- ph
2		biimt 325	. 2 |- (ph -> (ps <-> (ph -> ps)))
3	1, 2	ax-mp 8	1 |- (ps <-> (ph -> ps))

Syntax hints:   -> wi 4   <-> wb 176

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

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  mt2bi  328  pm4.83  895  truimfal  1345  equsalhw  1838  equveli  1988  sbequ8  2079  ralv  2872  ssopr  4846