Metamath Proof Explorer

Theorem frege54cor1a

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

Ref Expression
Assertion frege54cor1a 
|- if- ( ph , ph , -. ph )

Proof

Step Hyp Ref Expression
1 ax-frege54a 
 |-  ( ph <-> ph )
2 frege54cor0a 
 |-  ( ( ph <-> ph ) <-> if- ( ph , ph , -. ph ) )
3 1 2 mpbi 
 |-  if- ( ph , ph , -. ph )