Theorem exp45 303

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 294	. 2 |- (ph -> (ps -> ((ch /\ th) -> ta )))
3	2	exp4a 295	1 |- (ph -> (ps -> (ch -> (th -> ta ))))

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  oaass 3163  zornlem4 3606  zornlem7 3609  spansncv 5542  mdsymlem5 5780

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

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