Theorem frege54cor1a

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

	Ref	Expression
Assertion	frege54cor1a	$$⊢if-\left(\phi ,\phi ,\neg \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		ax-frege54a	$$⊢\phi \leftrightarrow \phi$$
2		frege54cor0a	$$⊢\left(\phi \leftrightarrow \phi \right)\leftrightarrow if-\left(\phi ,\phi ,\neg \phi \right)$$
3	1 2	mpbi	$$⊢if-\left(\phi ,\phi ,\neg \phi \right)$$