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Theorem bj-consensusALT 32869
 Description: Alternate proof of bj-consensus 32868. (Contributed by BJ, 30-Sep-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
bj-consensusALT ((if-(𝜑, 𝜓, 𝜒) ∨ (𝜓𝜒)) ↔ if-(𝜑, 𝜓, 𝜒))

Proof of Theorem bj-consensusALT
StepHypRef Expression
1 orcom 401 . 2 ((if-(𝜑, 𝜓, 𝜒) ∨ (𝜓𝜒)) ↔ ((𝜓𝜒) ∨ if-(𝜑, 𝜓, 𝜒)))
2 anifp 1058 . . 3 ((𝜓𝜒) → if-(𝜑, 𝜓, 𝜒))
3 pm4.72 956 . . 3 (((𝜓𝜒) → if-(𝜑, 𝜓, 𝜒)) ↔ (if-(𝜑, 𝜓, 𝜒) ↔ ((𝜓𝜒) ∨ if-(𝜑, 𝜓, 𝜒))))
42, 3mpbi 220 . 2 (if-(𝜑, 𝜓, 𝜒) ↔ ((𝜓𝜒) ∨ if-(𝜑, 𝜓, 𝜒)))
51, 4bitr4i 267 1 ((if-(𝜑, 𝜓, 𝜒) ∨ (𝜓𝜒)) ↔ if-(𝜑, 𝜓, 𝜒))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196   ∨ wo 382   ∧ wa 383  if-wif 1050 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-or 384  df-an 385  df-ifp 1051 This theorem is referenced by: (None)
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