Theorem exp4b 367

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 115	. 2 |- ( ph -> ( ps -> ( ( ch /\ th ) -> ta ) ) )
3	2	exp4a 366	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:  exp43  372  reuss2  3513  nndi  6749  mulnqprl  7925  mulnqpru  7926  distrlem5prl  7943  distrlem5pru  7944  recexprlemss1l  7992  recexprlemss1u  7993  lemul12a  9182  nnmulcl  9304  elfz0fzfz0  10511  fzo1fzo0n0  10573  fzofzim  10578  elincfzoext  10589  elfzodifsumelfzo  10597  le2sq2  11030  swrdswrd  11455  swrdccat3blem  11489  oddprmgt2  12890  infpnlem1  13116  lmodvsdi  14620