Theorem exp41 299

Description: An exportation inference.

Hypothesis

Ref	Expression
exp41.1	|- ((((ph /\ ps) /\ ch) /\ th) -> ta )

Assertion

Ref	Expression
exp41	|- (ph -> (ps -> (ch -> (th -> ta ))))

Proof of Theorem exp41

Step	Hyp	Ref	Expression
1		exp41.1	. . 3 |- ((((ph /\ ps) /\ ch) /\ th) -> ta )
2	1	exp 291	. 2 |- (((ph /\ ps) /\ ch) -> (th -> ta ))
3	2	exp31 293	1 |- (ph -> (ps -> (ch -> (th -> ta ))))

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  tz7.49 2997  infxpidmlem12 4944  osumlem4 5533

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