Theorem exp4a 589

Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)

Hypothesis

Ref	Expression
exp4a.1	|- (ph -> (ps -> ((ch /\ th) -> ta)))

Assertion

Ref	Expression
exp4a	|- (ph -> (ps -> (ch -> (th -> ta))))

Proof of Theorem exp4a

Step	Hyp	Ref	Expression
1		exp4a.1	. 2 |- (ph -> (ps -> ((ch /\ th) -> ta)))
2		impexp 433	. 2 |- (((ch /\ th) -> ta) <-> (ch -> (th -> ta)))
3	1, 2	syl6ib 217	1 |- (ph -> (ps -> (ch -> (th -> ta))))

Syntax hints:   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is referenced by:  exp4b  590  exp4d  592  exp45  597  exp5c  599  spfininduct  4541  fununiq  5518  fntxp  5805