Theorem 3exp1 1254

Description: Exportation from left triple conjunction. (Contributed by NM, 24-Feb-2005.)

Hypothesis

Ref	Expression
3exp1.1	|- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )

Assertion

Ref	Expression
3exp1	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Proof of Theorem 3exp1

Step	Hyp	Ref	Expression
1		3exp1.1	. . 3 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )
2	1	ex 115	. 2 |- ( ( ph /\ ps /\ ch ) -> ( th -> ta ) )
3	2	3exp 1233	1 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  ltmpig  7706  mulgaddcom  13949  mulginvcom  13950