Theorem bj-sbtv 31954

Description: Version of sbt 2407 with a dv condition, which does not require ax-13 2234. (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		bj-stdpc4v 31942	. 2 ⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
2		bj-sbtv.1	. 2 ⊢ 𝜑
3	1, 2	mpg 1715	1 ⊢ [𝑦 / 𝑥]𝜑

Syntax hints:  [wsb 1867

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-sb 1868

This theorem is referenced by:  bj-vjust  31974