Theorem exp43 354

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

Hypothesis

Ref	Expression
exp43.1	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) -> ta )

Assertion

Ref	Expression
exp43	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Proof of Theorem exp43

Step	Hyp	Ref	Expression
1		exp43.1	. . 3 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) -> ta )
2	1	ex 108	. 2 |- ( ( ph /\ ps ) -> ( ( ch /\ th ) -> ta ) )
3	2	exp4b 349	1 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Syntax hints:   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  exp53  359  funssres  4942  fvopab3ig  5246  fvmptt  5262  tfri3  5953  nnmordi  6089  ordiso2  6357  qaddcl  8570  qmulcl  8572  bernneq  9369