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Theorem an31 836
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 835 . 2 ((𝜑 ∧ (𝜓𝜒)) ↔ (𝜒 ∧ (𝜓𝜑)))
2 anass 678 . 2 (((𝜑𝜓) ∧ 𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
3 anass 678 . 2 (((𝜒𝜓) ∧ 𝜑) ↔ (𝜒 ∧ (𝜓𝜑)))
41, 2, 33bitr4i 290 1 (((𝜑𝜓) ∧ 𝜒) ↔ ((𝜒𝜓) ∧ 𝜑))
Colors of variables: wff setvar class
Syntax hints:  wb 194  wa 382
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 195  df-an 384
This theorem is referenced by:  euind  3359  reuind  3377  dchrelbas3  24707  lhpexle3  34099  4an31  37508  abciffcbatnabciffncba  39528
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