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  3484  nndi  6630  mulnqprl  7751  mulnqpru  7752  distrlem5prl  7769  distrlem5pru  7770  recexprlemss1l  7818  recexprlemss1u  7819  lemul12a  9005  nnmulcl  9127  elfz0fzfz0  10318  fzo1fzo0n0  10379  fzofzim  10384  elincfzoext  10394  elfzodifsumelfzo  10402  le2sq2  10832  swrdswrd  11232  swrdccat3blem  11266  oddprmgt2  12651  infpnlem1  12877  lmodvsdi  14269