Theorem imp42 369

Description: An importation inference.

Hypothesis

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

Assertion

Ref	Expression
imp42	|- (((ph /\ (ps /\ ch)) /\ th) -> ta)

Proof of Theorem imp42

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 |- (ph -> (ps -> (ch -> (th -> ta))))
2	1	imp32 363	. 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:  adantlrl 398  adantlrr 399  mapenlem2 4479  ltexprlem7 5131  reclem3pr 5141  bccl2t 6924  reccnv 7170  cvgratlem2 7203  fsum0diag2 7211  tgss2t 7597  grprcan 8025  irredlem1 10273

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