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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 (((𝜑𝜓) ∧ 𝜒) ↔ ((𝜑𝜒) ∧ 𝜓))

Proof of Theorem an32
StepHypRef Expression
1 anass 381 . 2 (((𝜑𝜓) ∧ 𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
2 an12 495 . 2 ((𝜑 ∧ (𝜓𝜒)) ↔ (𝜓 ∧ (𝜑𝜒)))
3 ancom 253 . 2 ((𝜓 ∧ (𝜑𝜒)) ↔ ((𝜑𝜒) ∧ 𝜓))
41, 2, 33bitri 195 1 (((𝜑𝜓) ∧ 𝜒) ↔ ((𝜑𝜒) ∧ 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  896  indifdir  3193  inrab2  3210  reupick  3221  unidif0  3920  resco  4825  f11o  5159  respreima  5295  dff1o6  5416  dfoprab2  5552  xpassen  6304  enq0enq  6527  elioomnf  8835
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