Theorem adantllr 481

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

Proof of Theorem adantllr

Step	Hyp	Ref	Expression
1		simpl 109	. 2 |- ( ( ph /\ ta ) -> ph )
2		adantl2.1	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	1, 2	sylanl1 402	1 |- ( ( ( ( ph /\ ta ) /\ ps ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  ad4ant13  513  ad4ant134  1219  ad5ant145  1246  r19.29an  2636  diffifi  6952  fimax2gtrilemstep  6958  cnegexlem3  8198  cnegex  8199  lemul12b  8882  climshftlemg  11448  prodeq2  11703  fprodmodd  11787  lcmdvds  12220  pw2dvdslemn  12306  dfgrp3mlem  13173  tgcl  14243  metss  14673  mpomulcn  14745  ivthinclemlr  14816  ivthinclemur  14818