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  3461  nndi  6595  mulnqprl  7716  mulnqpru  7717  distrlem5prl  7734  distrlem5pru  7735  recexprlemss1l  7783  recexprlemss1u  7784  lemul12a  8970  nnmulcl  9092  elfz0fzfz0  10283  fzo1fzo0n0  10344  fzofzim  10349  elincfzoext  10359  elfzodifsumelfzo  10367  le2sq2  10797  swrdswrd  11196  swrdccat3blem  11230  oddprmgt2  12571  infpnlem1  12797  lmodvsdi  14188