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Theorem bnj257 31876
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj257 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜓𝜃𝜒))

Proof of Theorem bnj257
StepHypRef Expression
1 ancom 461 . . 3 ((𝜒𝜃) ↔ (𝜃𝜒))
21anbi2i 622 . 2 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜓) ∧ (𝜃𝜒)))
3 bnj256 31875 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ (𝜒𝜃)))
4 bnj256 31875 . 2 ((𝜑𝜓𝜃𝜒) ↔ ((𝜑𝜓) ∧ (𝜃𝜒)))
52, 3, 43bitr4i 304 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜓𝜃𝜒))
Colors of variables: wff setvar class
Syntax hints:  wb 207  wa 396  w-bnj17 31855
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 208  df-an 397  df-3an 1081  df-bnj17 31856
This theorem is referenced by:  bnj258  31877  bnj334  31882  bnj543  32064  bnj929  32107
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