Theorem exp45 386

Description: An exportation inference.

Hypothesis

Ref	Expression
exp45.1	|- ((ph /\ (ps /\ (ch /\ th))) -> ta)

Assertion

Ref	Expression
exp45	|- (ph -> (ps -> (ch -> (th -> ta))))

Proof of Theorem exp45

Step	Hyp	Ref	Expression
1		exp45.1	. . 3 |- ((ph /\ (ps /\ (ch /\ th))) -> ta)
2	1	exp32 377	. 2 |- (ph -> (ps -> ((ch /\ th) -> ta)))
3	2	exp4a 378	1 |- (ph -> (ps -> (ch -> (th -> ta))))

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  oaass 4195  zorn2lem4 4791  zorn2lem7 4794  cvgratlem2 7251  metcnpi3 7892  metcnpi4 7893  metcni2 7895  bcthlem21 8019  grprcan 8063  spansncv 9597  mdsymlem5 10334

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain