Theorem adantlrr 474

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

Hypothesis

Ref	Expression
adantl2.1	|- ( ( ( ph /\ ps ) /\ ch ) -> th )

Assertion

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

Proof of Theorem adantlrr

Step	Hyp	Ref	Expression
1		simpl 108	. 2 |- ( ( ps /\ ta ) -> ps )
2		adantl2.1	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	1, 2	sylanl2 400	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:  exmidfodomrlemim  7050  distrlem1prl  7383  distrlem1pru  7384  cnegex  7933  lcmgcdlem  11747  lcmdvds  11749  metss2lem  12655