Theorem expimpd 586

Description: Exportation followed by a deduction version of importation. (Contributed by NM, 6-Sep-2008.)

Hypothesis

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

Assertion

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

Proof of Theorem expimpd

Step	Hyp	Ref	Expression
1		expimpd.1	. . 3 |- ((ph /\ ps) -> (ch -> th))
2	1	ex 423	. 2 |- (ph -> (ps -> (ch -> th)))
3	2	imp3a 420	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:  tfindi  4497  elpreima  5408  enmap2lem3  6066  enmap1lem3  6072  ncdisjun  6137  ncssfin  6152  leltctr  6213  letc  6232  nchoicelem8  6297  nchoicelem12  6301