Theorem 3expd 1155

Description: Exportation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)

Hypothesis

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

Assertion

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

Proof of Theorem 3expd

Step	Hyp	Ref	Expression
1		3expd.1	. . . 4 |- ( ph -> ( ( ps /\ ch /\ th ) -> ta ) )
2	1	com12 30	. . 3 |- ( ( ps /\ ch /\ th ) -> ( ph -> ta ) )
3	2	3exp 1137	. 2 |- ( ps -> ( ch -> ( th -> ( ph -> ta ) ) ) )
4	3	com4r 85	1 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Syntax hints:   -> wi 4   /\ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by:  3exp2  1156  exp516  1158  3impexp  1366  3impexpbicom  1367