Theorem 3adant2r 1165

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Hypothesis

Ref	Expression
3adant1l.1	|- ( ( ph /\ ps /\ ch ) -> th )

Assertion

Ref	Expression
3adant2r	|- ( ( ph /\ ( ps /\ ta ) /\ ch ) -> th )

Proof of Theorem 3adant2r

Step	Hyp	Ref	Expression
1		3adant1l.1	. . . 4 |- ( ( ph /\ ps /\ ch ) -> th )
2	1	3com12 1143	. . 3 |- ( ( ps /\ ph /\ ch ) -> th )
3	2	3adant1r 1163	. 2 |- ( ( ( ps /\ ta ) /\ ph /\ ch ) -> th )
4	3	3com12 1143	1 |- ( ( ph /\ ( ps /\ ta ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 102   /\ w3a 920

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 922

This theorem is referenced by:  caovimo  5725  mulassnqg  6636  prarloc  6755  ltexprlemfl  6861  ltexprlemfu  6863  addasssrg  6995  axaddass  7100