Theorem frege54cor1a

Description: Reflexive equality. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege54cor1a	⊢ if- ( 𝜑 , 𝜑 , ¬ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		ax-frege54a	⊢ ( 𝜑 ↔ 𝜑 )
2		frege54cor0a	⊢ ( ( 𝜑 ↔ 𝜑 ) ↔ if- ( 𝜑 , 𝜑 , ¬ 𝜑 ) )
3	1 2	mpbi	⊢ if- ( 𝜑 , 𝜑 , ¬ 𝜑 )