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  7064  fimax2gtrilemstep  7071  cnegexlem3  8334  cnegex  8335  lemul12b  9019  climshftlemg  11828  prodeq2  12083  fprodmodd  12167  lcmdvds  12616  pw2dvdslemn  12702  dfgrp3mlem  13646  tgcl  14753  metss  15183  mpomulcn  15255  ivthinclemlr  15326  ivthinclemur  15328  nnnninfex  16448