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  1244  ad5ant145  1271  r19.29an  2685  diffifi  7151  fimax2gtrilemstep  7158  cnegexlem3  8450  cnegex  8451  lemul12b  9135  climshftlemg  11987  prodeq2  12243  fprodmodd  12327  lcmdvds  12776  pw2dvdslemn  12862  dfgrp3mlem  13811  tgcl  14929  metss  15359  mpomulcn  15431  ivthinclemlr  15502  ivthinclemur  15504  nnnninfex  16800