Theorem bj-nfs1v 37507

Description: Version of nfsb2 2517 with a disjoint variable condition, which does not require ax-13 2406, and removal of ax-13 2406 from nfs1v 2194. (Contributed by BJ, 24-Jun-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-nfs1v	⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑

Distinct variable group:   𝑥,𝑦

Allowed substitution hints:   𝜑(𝑥, 𝑦)

Proof of Theorem bj-nfs1v

Step	Hyp	Ref	Expression
1		bj-hbs1 37506	. 2 ⊢ ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑)
2	1	nf5i 2184	1 ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑

This proof depends on syntax axioms:  Ⅎwnf 1816  [wsb 2099

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-10 2179  ax-12 2216

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-ex 1813  df-nf 1817  df-sb 2100

This theorem is used by: (None)