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Theorem an42 521
Description: Rearrangement of 4 conjuncts. (Contributed by NM, 7-Feb-1996.)
Assertion
Ref Expression
an42 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜒) ∧ (𝜃𝜓)))

Proof of Theorem an42
StepHypRef Expression
1 an4 520 . 2 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜒) ∧ (𝜓𝜃)))
2 ancom 253 . . 3 ((𝜓𝜃) ↔ (𝜃𝜓))
32anbi2i 430 . 2 (((𝜑𝜒) ∧ (𝜓𝜃)) ↔ ((𝜑𝜒) ∧ (𝜃𝜓)))
41, 3bitri 173 1 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜒) ∧ (𝜃𝜓)))
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:  rnlem  883  distrnqg  6466  distrnq0  6538  prcdnql  6563  prcunqu  6564
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