Theorem bj-sbtv 33290

Description: Version of sbt 2551 with a disjoint variable condition, which does not require ax-13 2389. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-sbtv.1	⊢ 𝜑

Assertion

Ref	Expression
bj-sbtv	⊢ [𝑦 / 𝑥]𝜑

Distinct variable group:   𝑥,𝑦

Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem bj-sbtv

Step	Hyp	Ref	Expression
1		stdpc4v 2301	. 2 ⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
2		bj-sbtv.1	. 2 ⊢ 𝜑
3	1, 2	mpg 1896	1 ⊢ [𝑦 / 𝑥]𝜑

Syntax hints:  [wsb 2067

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-12 2220

This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1879  df-sb 2068

This theorem is referenced by:  bj-vjust  33308