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  1241  ad5ant145  1268  r19.29an  2673  diffifi  7064  fimax2gtrilemstep  7070  cnegexlem3  8331  cnegex  8332  lemul12b  9016  climshftlemg  11821  prodeq2  12076  fprodmodd  12160  lcmdvds  12609  pw2dvdslemn  12695  dfgrp3mlem  13639  tgcl  14746  metss  15176  mpomulcn  15248  ivthinclemlr  15319  ivthinclemur  15321  nnnninfex  16418