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Theorem an32 773
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 630 . 2 (((φ ψ) χ) ↔ (φ (ψ χ)))
2 an12 772 . 2 ((φ (ψ χ)) ↔ (ψ (φ χ)))
3 ancom 437 . 2 ((ψ (φ χ)) ↔ ((φ χ) ψ))
41, 2, 33bitri 262 1 (((φ ψ) χ) ↔ ((φ χ) ψ))
Colors of variables: wff setvar class
Syntax hints:  wb 176   wa 358
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 177  df-an 360
This theorem is referenced by:  an32s  779  3anan32  946  indifdir  3511  inrab2  3528  reupick  3539  resco  5085  imadif  5171  dff1o3  5292  f11o  5315  respreima  5410  dff1o6  5475  brpprod  5839
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