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	⊢ (((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 402	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  513  ad4ant134  1219  ad5ant145  1246  r19.29an  2639  diffifi  6964  fimax2gtrilemstep  6970  cnegexlem3  8220  cnegex  8221  lemul12b  8905  climshftlemg  11484  prodeq2  11739  fprodmodd  11823  lcmdvds  12272  pw2dvdslemn  12358  dfgrp3mlem  13300  tgcl  14384  metss  14814  mpomulcn  14886  ivthinclemlr  14957  ivthinclemur  14959