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

Metamath Proof Explorer

Theorem bj-nfs1v

Description: Version of nfsb2 with a disjoint variable condition, which does not require ax-13 , and removal of ax-13 from nfs1v . (Contributed by BJ, 24-Jun-2019) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	bj-nfs1v	⊢ Ⅎ 𝑥 [ 𝑦 / 𝑥 ] 𝜑

Proof

Step	Hyp	Ref	Expression
1		bj-hbs1	⊢ ( [ 𝑦 / 𝑥 ] 𝜑 → ∀ 𝑥 [ 𝑦 / 𝑥 ] 𝜑 )
2	1	nf5i	⊢ Ⅎ 𝑥 [ 𝑦 / 𝑥 ] 𝜑