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  3487  nndi  6653  mulnqprl  7787  mulnqpru  7788  distrlem5prl  7805  distrlem5pru  7806  recexprlemss1l  7854  recexprlemss1u  7855  lemul12a  9041  nnmulcl  9163  elfz0fzfz0  10360  fzo1fzo0n0  10421  fzofzim  10426  elincfzoext  10437  elfzodifsumelfzo  10445  le2sq2  10876  swrdswrd  11285  swrdccat3blem  11319  oddprmgt2  12705  infpnlem1  12931  lmodvsdi  14324