Theorem adantllr 485

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	⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
adantllr	⊢ ((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem adantllr

Step	Hyp	Ref	Expression
1		simpl 109	. 2 ⊢ ((𝜑 ∧ 𝜏) → 𝜑)
2		adantl2.1	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)
3	1, 2	sylanl1 406	1 ⊢ ((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)

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  517  ad4ant134  1248  ad5ant145  1275  r19.29an  2693  diffifi  7192  fimax2gtrilemstep  7199  cnegexlem3  8497  cnegex  8498  lemul12b  9185  climshftlemg  12051  prodeq2  12307  fprodmodd  12391  lcmdvds  12840  pw2dvdslemn  12926  dfgrp3mlem  13886  tgcl  15148  metss  15578  mpomulcn  15650  ivthinclemlr  15721  ivthinclemur  15723  nnnninfex  17039