Theorem exp44 302

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 294	. 2 |- (ph -> ((ps /\ ch) -> (th -> ta )))
3	2	exp3a 292	1 |- (ph -> (ps -> (ch -> (th -> ta ))))

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  po2nr 2135  wefrc 2195  tz7.7 2224  oalimcl 3162  mapunen 3397  reclem3pr 3952  div23t 4240  spansncv 5542  atom1d 5750

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

metamath.org