Theorem imp45 372

Description: An importation inference.

Hypothesis

Ref	Expression
imp4.1	|- (ph -> (ps -> (ch -> (th -> ta))))

Assertion

Ref	Expression
imp45	|- ((ph /\ (ps /\ (ch /\ th))) -> ta)

Proof of Theorem imp45

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 |- (ph -> (ps -> (ch -> (th -> ta))))
2	1	imp4d 367	. 2 |- (ph -> ((ps /\ (ch /\ th)) -> ta))
3	2	imp 350	1 |- ((ph /\ (ps /\ (ch /\ th))) -> ta)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  adantrrl 402  adantrrr 403  prlem936b 5134  metcnpi3 7844  metcnpi4 7845  metcni2 7847  bcthlem21 7969  bcthlem29 7977  spansncv 9537  atcvatlem 10249

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