Theorem exbiri 382

Description: Inference form of exbir 1486. (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 297	. 2 |- ( ( ( ph /\ ps ) /\ th ) -> ch )
3	2	exp31 364	1 |- ( ph -> ( ps -> ( th -> ch ) ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   <-> wb 105

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  biimp3ar  1387  eqrdav  2237  tfrlem9  6590  mapfset  6945  sbthlem1  7274  lbreu  9275  uzsubsubfz  10452  elfzodifsumelfzo  10619  pfxccatin12lem3  11504  cncfmptid  15698  addccncf  15701  negcncf  15706  gausslemma2dlem1a  16177  usgredg2vlem2  16464  clwwlkccatlem  16641