Theorem 3exp2 1256

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 1255	1 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1009

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 1011

This theorem is referenced by:  3anassrs  1260  po2nr  4449  fliftfund  5993  tfrlemibxssdm  6588  tfr1onlembxssdm  6604  tfrcllembxssdm  6617  imasmnd2  13736  grpinveu  13820  grpid  13821  grpasscan1  13845  imasgrp2  13890  imasrng  14230  imasring  14342  islmodd  14602  islssmd  14668  mulgghm2  14915  isxmetd  15371  dvidlemap  15715  dvidrelem  15716  dvidsslem  15717