Theorem exp45 395

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 386	. 2 |- (ph -> (ps -> ((ch /\ th) -> ta)))
3	2	exp4a 387	1 |- (ph -> (ps -> (ch -> (th -> ta))))

Syntax hints:   -> wi 3   /\ wa 230

This theorem is referenced by:  oaass 4253  zorn2lem4 4853  zorn2lem7 4856  cvgratlem2 7341  metcnpi3 7977  metcnpi4 7978  metcni2 7980  bcthlem21 8104  grprcan 8147  spansncvi 9680  mdsymlem5 10418

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 154  df-an 232

Copyright terms: Public domain