Theorem exp44 385

Description: An exportation inference.

Hypothesis

Ref	Expression
exp44.1	|- ((ph /\ ((ps /\ ch) /\ th)) -> ta)

Assertion

Ref	Expression
exp44	|- (ph -> (ps -> (ch -> (th -> ta))))

Proof of Theorem exp44

Step	Hyp	Ref	Expression
1		exp44.1	. . 3 |- ((ph /\ ((ps /\ ch) /\ th)) -> ta)
2	1	exp32 377	. 2 |- (ph -> ((ps /\ ch) -> (th -> ta)))
3	2	exp3a 375	1 |- (ph -> (ps -> (ch -> (th -> ta))))

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  wefrc 2943  tz7.7 2973  oalimcl 4194  mapunen 4502  reclem3pr 5158  unbenlem 7504  lmcau 7996  ubthlem14 8542  spansncv 9597  atom1d 10280  irredlem3 10319

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