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Theorem bnj312 31085
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 1084 . . 3 ((𝜑𝜓𝜒) ↔ (𝜓𝜑𝜒))
21anbi1i 733 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) ↔ ((𝜓𝜑𝜒) ∧ 𝜃))
3 df-bnj17 31060 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓𝜒) ∧ 𝜃))
4 df-bnj17 31060 . 2 ((𝜓𝜑𝜒𝜃) ↔ ((𝜓𝜑𝜒) ∧ 𝜃))
52, 3, 43bitr4i 292 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜓𝜑𝜒𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 383  w3a 1072  w-bnj17 31059
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 385  df-3an 1074  df-bnj17 31060
This theorem is referenced by:  bnj334  31086  bnj563  31118  bnj953  31314
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