Theorem adantrrr 478

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)

Hypothesis

Ref	Expression
adantr2.1	|- ( ( ph /\ ( ps /\ ch ) ) -> th )

Assertion

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

Proof of Theorem adantrrr

Step	Hyp	Ref	Expression
1		simpl 108	. 2 |- ( ( ch /\ ta ) -> ch )
2		adantr2.1	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	1, 2	sylanr2 402	1 |- ( ( ph /\ ( ps /\ ( ch /\ ta ) ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 103

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 is referenced by:  2ndconst  6112  genpdisj  7324  ltexprlemdisj  7407  addsrmo  7544  mulsrmo  7545  axpre-suploclemres  7702  lemul12b  8612  tgcl  12222  neissex  12323