Theorem exbiri 374

Description: Inference form of exbir 1365. (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 291	. 2 |- ( ( ( ph /\ ps ) /\ th ) -> ch )
3	2	exp31 356	1 |- ( ph -> ( ps -> ( th -> ch ) ) )

Syntax hints:   -> wi 4   /\ wa 102   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  biimp3ar  1277  eqrdav  2080  tfrlem9  5958  lbreu  8023  uzsubsubfz  9066  elfzodifsumelfzo  9210