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  1241  ad5ant145  1268  r19.29an  2673  diffifi  7052  fimax2gtrilemstep  7058  cnegexlem3  8319  cnegex  8320  lemul12b  9004  climshftlemg  11808  prodeq2  12063  fprodmodd  12147  lcmdvds  12596  pw2dvdslemn  12682  dfgrp3mlem  13626  tgcl  14732  metss  15162  mpomulcn  15234  ivthinclemlr  15305  ivthinclemur  15307  nnnninfex  16347