Theorem adantlrr 487

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 109	. 2 |- ( ( ps /\ ta ) -> ps )
2		adantl2.1	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	1, 2	sylanl2 407	1 |- ( ( ( ph /\ ( ps /\ ta ) ) /\ ch ) -> th )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is used by:  exmidfodomrlemim  7553  distrlem1prl  7949  distrlem1pru  7950  cnegex  8504  lcmgcdlem  12855  lcmdvds  12857  ballotfilemfc0  13232  ballotfilemfcc  13233  conjnmzb  14083  metss2lem  15598  dvmptfsum  15826