Theorem bj-nfs1v 34532

Description: Version of nfsb2 2502 with a disjoint variable condition, which does not require ax-13 2380, and removal of ax-13 2380 from nfs1v 2158. (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 34531	. 2 ⊢ ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑)
2	1	nf5i 2148	1 ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1786  [wsb 2070

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-10 2143  ax-12 2176

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 846  df-ex 1783  df-nf 1787  df-sb 2071

This theorem is referenced by: (None)