Theorem ifpbiidcor 39833

Description: Restatement of biid 263. (Contributed by RP, 25-Apr-2020.)

Assertion

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

Proof of Theorem ifpbiidcor

Step	Hyp	Ref	Expression
1		biid 263	. 2 ⊢ (𝜑 ↔ 𝜑)
2		ifpdfbi 39832	. 2 ⊢ ((𝜑 ↔ 𝜑) ↔ if-(𝜑, 𝜑, ¬ 𝜑))
3	1, 2	mpbi 232	1 ⊢ if-(𝜑, 𝜑, ¬ 𝜑)

Syntax hints:  ¬ wn 3   ↔ wb 208  if-wif 1057

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

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-ifp 1058  df-tru 1536

This theorem is referenced by:  ifpbiidcor2  39842