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Metamath Proof Explorer

Theorem dfifp4

Description: Alternate definition of the conditional operator for propositions. (Contributed by BJ, 30-Sep-2019)

Ref Expression
Assertion dfifp4 ⊢ if- φ ψ χ ↔ ¬ φ ∨ ψ ∧ φ ∨ χ

Proof

Step Hyp Ref Expression
1 dfifp3 ⊢ if- φ ψ χ ↔ φ → ψ ∧ φ ∨ χ
2 imor ⊢ φ → ψ ↔ ¬ φ ∨ ψ
3 1 2 bianbi ⊢ if- φ ψ χ ↔ ¬ φ ∨ ψ ∧ φ ∨ χ