This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem bj-drnf2v

Description: Version of drnf2 with a disjoint variable condition, which does not require ax-10 , ax-11 , ax-12 , ax-13 . Instance of nfbidv . Note that the version of axc15 with a disjoint variable condition is actually ax12v2 (up to adding a superfluous antecedent). (Contributed by BJ, 17-Jun-2019) (Proof modification is discouraged.)

		Ref	Expression
	Hypothesis	bj-drnf2v.1	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
	Assertion	bj-drnf2v	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ( Ⅎ 𝑧 𝜑 ↔ Ⅎ 𝑧 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		bj-drnf2v.1	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
2	1	nfbidv	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ( Ⅎ 𝑧 𝜑 ↔ Ⅎ 𝑧 𝜓 ) )