Metamath Proof Explorer


Theorem idd

Description: Principle of identity id with antecedent. (Contributed by NM, 26-Nov-1995)

Ref Expression
Assertion idd ( 𝜑 → ( 𝜓 → 𝜓 ) )

Proof

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