Theorem ifpbiidcor2 39855

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

Assertion

Ref	Expression
ifpbiidcor2	⊢ ¬ if-(𝜑, ¬ 𝜑, 𝜑)

Proof of Theorem ifpbiidcor2

Step	Hyp	Ref	Expression
1		ifpbiidcor 39846	. 2 ⊢ if-(𝜑, 𝜑, ¬ 𝜑)
2		ifpnot23b 39854	. 2 ⊢ (¬ if-(𝜑, ¬ 𝜑, 𝜑) ↔ if-(𝜑, 𝜑, ¬ 𝜑))
3	1, 2	mpbir 233	1 ⊢ ¬ if-(𝜑, ¬ 𝜑, 𝜑)

Syntax hints:  ¬ wn 3  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 1539

This theorem is referenced by: (None)