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Theorem an31 486
Description: A rearrangement of conjuncts. (Contributed by NM, 24-Jun-2012.) (Proof shortened by Wolf Lammen, 31-Dec-2012.)
Assertion
Ref Expression
an31 (((φ ψ) χ) ↔ ((χ ψ) φ))

Proof of Theorem an31
StepHypRef Expression
1 an13 485 . 2 ((φ (ψ χ)) ↔ (χ (ψ φ)))
2 anass 383 . 2 (((φ ψ) χ) ↔ (φ (ψ χ)))
3 anass 383 . 2 (((χ ψ) φ) ↔ (χ (ψ φ)))
41, 2, 33bitr4i 201 1 (((φ ψ) χ) ↔ ((χ ψ) φ))
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  euind  2701  reuind  2717
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