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Theorem an32 496
 Description: A rearrangement of conjuncts. (Contributed by NM, 12-Mar-1995.) (Proof shortened by Wolf Lammen, 25-Dec-2012.)
Assertion
Ref Expression
an32 (((φ ψ) χ) ↔ ((φ χ) ψ))

Proof of Theorem an32
StepHypRef Expression
1 anass 381 . 2 (((φ ψ) χ) ↔ (φ (ψ χ)))
2 an12 495 . 2 ((φ (ψ χ)) ↔ (ψ (φ χ)))
3 ancom 253 . 2 ((ψ (φ χ)) ↔ ((φ χ) ψ))
41, 2, 33bitri 195 1 (((φ ψ) χ) ↔ ((φ χ) ψ))
 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:  an32s  502  3anan32  895  indifdir  3187  inrab2  3204  reupick  3215  unidif0  3911  resco  4768  f11o  5102  respreima  5238  dff1o6  5359  dfoprab2  5494  xpassen  6240  enq0enq  6413  elioomnf  8587
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