Theorem 3exp2 1228

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 1227	1 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 981

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 983

This theorem is referenced by:  3anassrs  1232  po2nr  4357  fliftfund  5868  tfrlemibxssdm  6415  tfr1onlembxssdm  6431  tfrcllembxssdm  6444  imasmnd2  13317  grpinveu  13403  grpid  13404  grpasscan1  13428  imasgrp2  13479  imasrng  13751  imasring  13859  islmodd  14088  islssmd  14154  mulgghm2  14403  isxmetd  14852  dvidlemap  15196  dvidrelem  15197  dvidsslem  15198