Theorem exp31 587

Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)

Hypothesis

Ref	Expression
exp31.1	|- (((ph /\ ps) /\ ch) -> th)

Assertion

Ref	Expression
exp31	|- (ph -> (ps -> (ch -> th)))

Proof of Theorem exp31

Step	Hyp	Ref	Expression
1		exp31.1	. . 3 |- (((ph /\ ps) /\ ch) -> th)
2	1	ex 423	. 2 |- ((ph /\ ps) -> (ch -> th))
3	2	ex 423	1 |- (ph -> (ps -> (ch -> th)))

Syntax hints:   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  exp41  593  exp42  594  expl  601  exbiri  605  anasss  628  an31s  781  3impa  1146  exp516  1171  ax11indalem  2197  ax11inda2ALT  2198  nndisjeq  4430  dffo3  5423  fconstfv  5457