Theorem exp4b 590

Description: An exportation inference. (Contributed by NM, 26-Apr-1994.) (Proof shortened by Wolf Lammen, 23-Nov-2012.)

Hypothesis

Ref	Expression
exp4b.1	|- ((ph /\ ps) -> ((ch /\ th) -> ta))

Assertion

Ref	Expression
exp4b	|- (ph -> (ps -> (ch -> (th -> ta))))

Proof of Theorem exp4b

Step	Hyp	Ref	Expression
1		exp4b.1	. . 3 |- ((ph /\ ps) -> ((ch /\ th) -> ta))
2	1	ex 423	. 2 |- (ph -> (ps -> ((ch /\ th) -> ta)))
3	2	exp4a 589	1 |- (ph -> (ps -> (ch -> (th -> ta))))

This proof depends on syntax axioms:   -> wi 4   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is used by:  exp43  595  reuss2  3536  nchoicelem17  6306