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Metamath Proof Explorer

Theorem biidd

Description: Principle of identity with antecedent. (Contributed by NM, 25-Nov-1995)

Ref Expression
Assertion biidd ( 𝜑 → ( 𝜓 ↔ 𝜓 ) )

Proof

Step Hyp Ref Expression
1 biid ⊢ ( 𝜓 ↔ 𝜓 )
2 1 a1i ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜓 ) )