Metamath Proof Explorer


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