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Theorem an31 554
Description: A rearrangement of conjuncts. (Contributed by NM, 24-Jun-2012.) (Proof shortened by Wolf Lammen, 31-Dec-2012.)
Assertion
Ref Expression
an31 (((𝜑𝜓) ∧ 𝜒) ↔ ((𝜒𝜓) ∧ 𝜑))

Proof of Theorem an31
StepHypRef Expression
1 an13 553 . 2 ((𝜑 ∧ (𝜓𝜒)) ↔ (𝜒 ∧ (𝜓𝜑)))
2 anass 399 . 2 (((𝜑𝜓) ∧ 𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
3 anass 399 . 2 (((𝜒𝜓) ∧ 𝜑) ↔ (𝜒 ∧ (𝜓𝜑)))
41, 2, 33bitr4i 211 1 (((𝜑𝜓) ∧ 𝜒) ↔ ((𝜒𝜓) ∧ 𝜑))
Colors of variables: wff set class
Syntax hints:  wa 103  wb 104
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 depends on definitions:  df-bi 116
This theorem is referenced by:  euind  2875  reuind  2893
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