Theorem frege54cor1a 38158

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

Assertion

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

Proof of Theorem frege54cor1a

Step	Hyp	Ref	Expression
1		ax-frege54a 38156	. 2 |- ( ph <-> ph )
2		frege54cor0a 38157	. 2 |- ( ( ph <-> ph ) <-> if- ( ph , ph , -. ph ) )
3	1, 2	mpbi 220	1 |- if- ( ph , ph , -. ph )

Syntax hints:   -. wn 3   <-> wb 196  if-wif 1012

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege28 38124  ax-frege54a 38156

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ifp 1013

This theorem is referenced by:  frege55a  38162