Theorem exp520 1089

Description: A triple exportation inference. (Contributed by Jeff Hankins, 22-Sep-2009.)

Hypothesis

Ref	Expression
exp520.1	|- (((ph /\ ps /\ ch) /\ (th /\ ta)) -> et)

Assertion

Ref	Expression
exp520	|- (ph -> (ps -> (ch -> (th -> (ta -> et)))))

Proof of Theorem exp520

Step	Hyp	Ref	Expression
1		exp520.1	. . 3 |- (((ph /\ ps /\ ch) /\ (th /\ ta)) -> et)
2	1	ex 402	. 2 |- ((ph /\ ps /\ ch) -> ((th /\ ta) -> et))
3	2	exp5o 1087	1 |- (ph -> (ps -> (ch -> (th -> (ta -> et)))))

Syntax hints:   -> wi 3   /\ wa 240   /\ w3a 858

This theorem is referenced by:  omwordri 5251  oewordri 5267  hausfillim 10303

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 164  df-an 242  df-3an 860

Copyright terms: Public domain