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  3453  nndi  6572  mulnqprl  7681  mulnqpru  7682  distrlem5prl  7699  distrlem5pru  7700  recexprlemss1l  7748  recexprlemss1u  7749  lemul12a  8935  nnmulcl  9057  elfz0fzfz0  10248  fzo1fzo0n0  10307  fzofzim  10312  elincfzoext  10322  elfzodifsumelfzo  10330  le2sq2  10760  oddprmgt2  12456  infpnlem1  12682  lmodvsdi  14073