Theorem exbiri 364

Description: Inference form of exbir 1325. (Contributed by Alan Sare, 31-Dec-2011.) (Proof shortened by Wolf Lammen, 27-Jan-2013.)

Hypothesis

Ref	Expression
exbiri.1	|- ( ( ph /\ ps ) -> ( ch <-> th ) )

Assertion

Ref	Expression
exbiri	|- ( ph -> ( ps -> ( th -> ch ) ) )

Proof of Theorem exbiri

Step	Hyp	Ref	Expression
1		exbiri.1	. . 3 |- ( ( ph /\ ps ) -> ( ch <-> th ) )
2	1	biimpar 281	. 2 |- ( ( ( ph /\ ps ) /\ th ) -> ch )
3	2	exp31 346	1 |- ( ph -> ( ps -> ( th -> ch ) ) )

Syntax hints:   -> wi 4   /\ wa 97   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  biimp3ar  1236  eqrdav  2039  tfrlem9  5935  uzsubsubfz  8911  elfzodifsumelfzo  9057