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  3501  nndi  6719  mulnqprl  7883  mulnqpru  7884  distrlem5prl  7901  distrlem5pru  7902  recexprlemss1l  7950  recexprlemss1u  7951  lemul12a  9136  nnmulcl  9258  elfz0fzfz0  10460  fzo1fzo0n0  10522  fzofzim  10527  elincfzoext  10538  elfzodifsumelfzo  10546  le2sq2  10977  swrdswrd  11397  swrdccat3blem  11431  oddprmgt2  12831  infpnlem1  13057  lmodvsdi  14459