Theorem exp42 300

Description: An exportation inference.

Hypothesis

Ref	Expression
exp42.1	|- (((ph /\ (ps /\ ch)) /\ th) -> ta )

Assertion

Ref	Expression
exp42	|- (ph -> (ps -> (ch -> (th -> ta ))))

Proof of Theorem exp42

Step	Hyp	Ref	Expression
1		exp42.1	. . 3 |- (((ph /\ (ps /\ ch)) /\ th) -> ta )
2	1	exp31 293	. 2 |- (ph -> ((ps /\ ch) -> (th -> ta )))
3	2	exp3a 292	1 |- (ph -> (ps -> (ch -> (th -> ta ))))

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  isofrlem 2939  oelim 3137  en3d 3304  zornlem7 3609  infxpidmlem11 4943  shscl 5282  spanun 5450

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org