Theorem bj-sbfv 32764

Description: Version of sbf 2380 with a dv condition, which does not require ax-13 2246. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-sbfv.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
bj-sbfv	⊢ ([𝑦 / 𝑥]𝜑 ↔ 𝜑)

Distinct variable group:   𝑥,𝑦

Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem bj-sbfv

Step	Hyp	Ref	Expression
1		bj-sbfv.1	. 2 ⊢ Ⅎ𝑥𝜑
2		bj-sbftv 32763	. 2 ⊢ (Ⅎ𝑥𝜑 → ([𝑦 / 𝑥]𝜑 ↔ 𝜑))
3	1, 2	ax-mp 5	1 ⊢ ([𝑦 / 𝑥]𝜑 ↔ 𝜑)

Syntax hints:   ↔ wb 196  Ⅎwnf 1708  [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-nf 1710  df-sb 1881

This theorem is referenced by: (None)