Theorem 3exp2 1225

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 1224	1 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 978

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 980

This theorem is referenced by:  3anassrs  1229  po2nr  4311  fliftfund  5800  tfrlemibxssdm  6330  tfr1onlembxssdm  6346  tfrcllembxssdm  6359  grpinveu  12916  grpid  12917  grpasscan1  12938  islmodd  13388  islssmd  13451  isxmetd  13932  dvidlemap  14245