Theorem 3imp2 1253

Description: Importation to right triple conjunction. (Contributed by NM, 26-Oct-2006.)

Hypothesis

Ref	Expression
3imp1.1	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Assertion

Ref	Expression
3imp2	|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )

Proof of Theorem 3imp2

Step	Hyp	Ref	Expression
1		3imp1.1	. . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2	1	3impd 1252	. 2 |- ( ph -> ( ( ps /\ ch /\ th ) -> ta ) )
3	2	imp 124	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

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

This theorem is used by:  ovg  6228  grplcan  13867  mulgnnass  13960  mulgass2  14363  lmodvsdi  14648  lmodvsdir  14649  lmodvsass  14650  lss1d  14720