Theorem exbiri 380

Description: Inference form of exbir 1424. (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 295	. 2 |- ( ( ( ph /\ ps ) /\ th ) -> ch )
3	2	exp31 362	1 |- ( ph -> ( ps -> ( th -> ch ) ) )

Syntax hints:   -> wi 4   /\ wa 103   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  biimp3ar  1336  eqrdav  2164  tfrlem9  6287  sbthlem1  6922  lbreu  8840  uzsubsubfz  9982  elfzodifsumelfzo  10136  cncfmptid  13223  addccncf  13226  negcncf  13228