Theorem 3exp2 1249

Description: Exportation from right triple conjunction. (Contributed by NM, 26-Oct-2006.)

Hypothesis

Ref	Expression
3exp2.1	|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )

Assertion

Ref	Expression
3exp2	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Proof of Theorem 3exp2

Step	Hyp	Ref	Expression
1		3exp2.1	. . 3 |- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )
2	1	ex 115	. 2 |- ( ph -> ( ( ps /\ ch /\ th ) -> ta ) )
3	2	3expd 1248	1 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1002

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  df-3an 1004

This theorem is referenced by:  3anassrs  1253  po2nr  4400  fliftfund  5927  tfrlemibxssdm  6479  tfr1onlembxssdm  6495  tfrcllembxssdm  6508  imasmnd2  13501  grpinveu  13587  grpid  13588  grpasscan1  13612  imasgrp2  13663  imasrng  13935  imasring  14043  islmodd  14273  islssmd  14339  mulgghm2  14588  isxmetd  15037  dvidlemap  15381  dvidrelem  15382  dvidsslem  15383