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Theorem 4an4132 38184
Description: A rearrangement of conjuncts for a 4-right-nested conjunction. (Contributed by Alan Sare, 30-May-2018.)
Hypothesis
Ref Expression
4an4132.1 ((((𝜃𝜒) ∧ 𝜓) ∧ 𝜑) → 𝜏)
Assertion
Ref Expression
4an4132 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)

Proof of Theorem 4an4132
StepHypRef Expression
1 simpr 477 . . 3 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜃)
2 simplr 791 . . 3 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜒)
31, 2jca 554 . 2 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → (𝜃𝜒))
4 simpllr 798 . 2 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜓)
5 simplll 797 . 2 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜑)
6 4an4132.1 . 2 ((((𝜃𝜒) ∧ 𝜓) ∧ 𝜑) → 𝜏)
73, 4, 5, 6syl21anc 1322 1 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
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
This theorem is referenced by:  sineq0ALT  38653
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