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Theorem bnj312 31868
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj312 ((𝜑𝜓𝜒𝜃) ↔ (𝜓𝜑𝜒𝜃))

Proof of Theorem bnj312
StepHypRef Expression
1 3ancoma 1092 . . 3 ((𝜑𝜓𝜒) ↔ (𝜓𝜑𝜒))
21anbi1i 623 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) ↔ ((𝜓𝜑𝜒) ∧ 𝜃))
3 df-bnj17 31843 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓𝜒) ∧ 𝜃))
4 df-bnj17 31843 . 2 ((𝜓𝜑𝜒𝜃) ↔ ((𝜓𝜑𝜒) ∧ 𝜃))
52, 3, 43bitr4i 304 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜓𝜑𝜒𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 207  wa 396  w3a 1081  w-bnj17 31842
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 1083  df-bnj17 31843
This theorem is referenced by:  bnj334  31869  bnj563  31900  bnj953  32097
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