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Theorem bnj257 30026
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 465 . . 3 ((𝜒𝜃) ↔ (𝜃𝜒))
21anbi2i 726 . 2 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜓) ∧ (𝜃𝜒)))
3 bnj256 30025 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ (𝜒𝜃)))
4 bnj256 30025 . 2 ((𝜑𝜓𝜃𝜒) ↔ ((𝜑𝜓) ∧ (𝜃𝜒)))
52, 3, 43bitr4i 291 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜓𝜃𝜒))
Colors of variables: wff setvar class
Syntax hints:  wb 195  wa 383  w-bnj17 30005
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 196  df-an 385  df-3an 1033  df-bnj17 30006
This theorem is referenced by:  bnj258  30027  bnj334  30032  bnj543  30217  bnj929  30260
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