Theorem ifpbiidcor 44433

Description: Restatement of biid 264. (Contributed by RP, 25-Apr-2020.)

Assertion

Ref	Expression
ifpbiidcor	⊢ if-(𝜑, 𝜑, ¬ 𝜑)

Proof of Theorem ifpbiidcor

Step	Hyp	Ref	Expression
1		biid 264	. 2 ⊢ (𝜑 ↔ 𝜑)
2		ifpdfbi 1086	. 2 ⊢ ((𝜑 ↔ 𝜑) ↔ if-(𝜑, 𝜑, ¬ 𝜑))
3	1, 2	mpbi 233	1 ⊢ if-(𝜑, 𝜑, ¬ 𝜑)

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 209  if-wif 1078

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-ifp 1079

This theorem is used by:  ifpbiidcor2  44442