Theorem exp43 372

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 115	. 2 |- ( ( ph /\ ps ) -> ( ( ch /\ th ) -> ta ) )
3	2	exp4b 367	1 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  exp53  377  funssres  5301  fvopab3ig  5636  fvmptt  5654  tfri3  6426  nnmordi  6575  fiintim  6993  ordiso2  7102  qaddcl  9711  qmulcl  9713  bernneq  10754  opnneissb  14401  txbas  14504