Theorem adantrrl 483

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
adantrrl	|- ( ( ph /\ ( ps /\ ( ta /\ ch ) ) ) -> th )

Proof of Theorem adantrrl

Step	Hyp	Ref	Expression
1		simpr 109	. 2 |- ( ( ta /\ ch ) -> ch )
2		adantr2.1	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	1, 2	sylanr2 403	1 |- ( ( ph /\ ( ps /\ ( ta /\ ch ) ) ) -> 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:  1stconst  6200  ltexprlemdisj  7568  axpre-suploclemres  7863  ltmul12a  8776  neiint  12939  neissex  12959