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  7076  fimax2gtrilemstep  7083  cnegexlem3  8346  cnegex  8347  lemul12b  9031  climshftlemg  11853  prodeq2  12108  fprodmodd  12192  lcmdvds  12641  pw2dvdslemn  12727  dfgrp3mlem  13671  tgcl  14778  metss  15208  mpomulcn  15280  ivthinclemlr  15351  ivthinclemur  15353  nnnninfex  16560