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Theorem 3adantlr3 38722
Description: Deduction adding a conjunct to antecedent. (Contributed by Glauco Siliprandi, 11-Dec-2019.)
Hypothesis
Ref Expression
3adantlr3.1 (((𝜑 ∧ (𝜓𝜒)) ∧ 𝜃) → 𝜏)
Assertion
Ref Expression
3adantlr3 (((𝜑 ∧ (𝜓𝜒𝜂)) ∧ 𝜃) → 𝜏)

Proof of Theorem 3adantlr3
StepHypRef Expression
1 simpll 789 . 2 (((𝜑 ∧ (𝜓𝜒𝜂)) ∧ 𝜃) → 𝜑)
2 simplr1 1101 . . 3 (((𝜑 ∧ (𝜓𝜒𝜂)) ∧ 𝜃) → 𝜓)
3 simplr2 1102 . . 3 (((𝜑 ∧ (𝜓𝜒𝜂)) ∧ 𝜃) → 𝜒)
42, 3jca 554 . 2 (((𝜑 ∧ (𝜓𝜒𝜂)) ∧ 𝜃) → (𝜓𝜒))
5 simpr 477 . 2 (((𝜑 ∧ (𝜓𝜒𝜂)) ∧ 𝜃) → 𝜃)
6 3adantlr3.1 . 2 (((𝜑 ∧ (𝜓𝜒)) ∧ 𝜃) → 𝜏)
71, 4, 5, 6syl21anc 1322 1 (((𝜑 ∧ (𝜓𝜒𝜂)) ∧ 𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1036
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1038
This theorem is referenced by:  fourierdlem42  39703
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