Theorem exp32 365

Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)

Hypothesis

Ref	Expression
exp32.1	|- ( ( ph /\ ( ps /\ ch ) ) -> th )

Assertion

Ref	Expression
exp32	|- ( ph -> ( ps -> ( ch -> th ) ) )

Proof of Theorem exp32

Step	Hyp	Ref	Expression
1		exp32.1	. . 3 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
2	1	ex 115	. 2 |- ( ph -> ( ( ps /\ ch ) -> th ) )
3	2	expd 258	1 |- ( ph -> ( ps -> ( ch -> th ) ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is used by:  exp44  373  exp45  374  expr  375  anassrs  404  an13s  573  3impb  1230  xordidc  1448  f0rn0  5587  funfvima3  5952  isoini  6024  ovg  6228  fundmen  7094  distrlem1prl  7949  distrlem1pru  7950  caucvgprprlemaddq  8075  recexgt0sr  8140  axpre-suploclemres  8268  cnegexlem2  8503  mulgt1  9195  faclbnd  11193  swrdwrdsymbg  11450  pfxccatin12lem2a  11513  pfxccat3  11520  swrdccat  11521  divgcdcoprm0  12895  cncongr2  12898  nnmaxpwlemdvds  12965  nnmaxpwlemndvds  12966  infpnlem1  13158  imasabl  14189  cnpnei  15369  dvmptfsum  15875  zabsle1  16216  lgsquad2lem2  16299  2lgsoddprm  16330  eupth2lemsfi  16817