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Metamath Proof Explorer

Theorem ifpid

Description: Value of the conditional operator for propositions when the same proposition is returned in either case. Analogue for propositions of ifid . This is essentially pm4.42 . (Contributed by BJ, 20-Sep-2019)

Ref Expression
Assertion ifpid ⊢ if- φ ψ ψ ↔ ψ

Proof

Step Hyp Ref Expression
1 ifptru ⊢ φ → if- φ ψ ψ ↔ ψ
2 ifpfal ⊢ ¬ φ → if- φ ψ ψ ↔ ψ
3 1 2 pm2.61i ⊢ if- φ ψ ψ ↔ ψ