Theorem 3exp2 1220

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 114	. 2 |- ( ph -> ( ( ps /\ ch /\ th ) -> ta ) )
3	2	3expd 1219	1 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 973

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 975

This theorem is referenced by:  3anassrs  1224  po2nr  4294  fliftfund  5776  tfrlemibxssdm  6306  tfr1onlembxssdm  6322  tfrcllembxssdm  6335  grpinveu  12741  grpid  12742  grpasscan1  12762  isxmetd  13141  dvidlemap  13454