Theorem exp43 370

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 114	. 2 |- ( ( ph /\ ps ) -> ( ( ch /\ th ) -> ta ) )
3	2	exp4b 365	1 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  exp53  375  funssres  5230  fvopab3ig  5560  fvmptt  5577  tfri3  6335  nnmordi  6484  fiintim  6894  ordiso2  7000  qaddcl  9573  qmulcl  9575  bernneq  10575  opnneissb  12795  txbas  12898