Theorem ifpbiidcor2 44269

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

Assertion

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

Proof of Theorem ifpbiidcor2

Step	Hyp	Ref	Expression
1		ifpbiidcor 44260	. 2 ⊢ if-(𝜑, 𝜑, ¬ 𝜑)
2		ifpnot23b 44268	. 2 ⊢ (¬ if-(𝜑, ¬ 𝜑, 𝜑) ↔ if-(𝜑, 𝜑, ¬ 𝜑))
3	1, 2	mpbir 234	1 ⊢ ¬ if-(𝜑, ¬ 𝜑, 𝜑)

This proof depends on syntax axioms:  ¬ wn 3  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: (None)