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 ) ) ) )

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:  exp43  372  reuss2  3513  nndi  6764  mulnqprl  7941  mulnqpru  7942  distrlem5prl  7959  distrlem5pru  7960  recexprlemss1l  8008  recexprlemss1u  8009  lemul12a  9200  nnmulcl  9334  elfz0fzfz0  10549  fzo1fzo0n0  10611  fzofzim  10616  elincfzoext  10627  elfzodifsumelfzo  10635  le2sq2  11072  swrdswrd  11498  swrdccat3blem  11532  oddprmgt2  12937  infpnlem1  13166  lmodvsdi  14756