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  3452  nndi  6571  mulnqprl  7680  mulnqpru  7681  distrlem5prl  7698  distrlem5pru  7699  recexprlemss1l  7747  recexprlemss1u  7748  lemul12a  8934  nnmulcl  9056  elfz0fzfz0  10247  fzo1fzo0n0  10305  fzofzim  10310  elincfzoext  10320  elfzodifsumelfzo  10328  le2sq2  10758  oddprmgt2  12427  infpnlem1  12653  lmodvsdi  14044