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Theorem bnj257 30480
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 466 . . 3 ((𝜒𝜃) ↔ (𝜃𝜒))
21anbi2i 729 . 2 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜓) ∧ (𝜃𝜒)))
3 bnj256 30479 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ (𝜒𝜃)))
4 bnj256 30479 . 2 ((𝜑𝜓𝜃𝜒) ↔ ((𝜑𝜓) ∧ (𝜃𝜒)))
52, 3, 43bitr4i 292 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜓𝜃𝜒))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 384  w-bnj17 30459
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 197  df-an 386  df-3an 1038  df-bnj17 30460
This theorem is referenced by:  bnj258  30481  bnj334  30486  bnj543  30671  bnj929  30714
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