Theorem exbiri 605

Description: Inference form of exbir 1365. This proof is exbiriVD in set.mm automatically translated and minimized. (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 471	. 2 |- (((ph /\ ps) /\ th) -> ch)
3	2	exp31 587	1 |- (ph -> (ps -> (th -> ch)))

This proof depends on syntax axioms:   -> wi 4   <-> wb 176   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  biimp3ar  1282  eqrdav  2352  ncfin  6248