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Theorem adantllr 470
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 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
adantllr ((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem adantllr
StepHypRef Expression
1 simpl 108 . 2 ((𝜑𝜏) → 𝜑)
2 adantl2.1 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
31, 2sylanl1 397 1 ((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  ad4ant134  1178  r19.29an  2549  diffifi  6754  fimax2gtrilemstep  6760  cnegexlem3  7903  cnegex  7904  lemul12b  8576  climshftlemg  11011  lcmdvds  11656  pw2dvdslemn  11738  tgcl  12128  metss  12558  ivthinclemlr  12679  ivthinclemur  12681
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