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 ) ) ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  exp53  377  funssres  5420  fvopab3ig  5779  fvmptt  5797  fvn0elsuppb  6492  tfri3  6638  nnmordi  6789  fiintim  7238  ordiso2  7375  qaddcl  10035  qmulcl  10037  bernneq  11098  opnneissb  15256  txbas  15359