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  3484  nndi  6640  mulnqprl  7766  mulnqpru  7767  distrlem5prl  7784  distrlem5pru  7785  recexprlemss1l  7833  recexprlemss1u  7834  lemul12a  9020  nnmulcl  9142  elfz0fzfz0  10334  fzo1fzo0n0  10395  fzofzim  10400  elincfzoext  10411  elfzodifsumelfzo  10419  le2sq2  10849  swrdswrd  11252  swrdccat3blem  11286  oddprmgt2  12671  infpnlem1  12897  lmodvsdi  14290