Theorem bj-sbtv 32766

Description: Version of sbt 2419 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-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 32754	. 2 ⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
2		bj-sbtv.1	. 2 ⊢ 𝜑
3	1, 2	mpg 1724	1 ⊢ [𝑦 / 𝑥]𝜑

Syntax hints:  [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-sb 1881

This theorem is referenced by:  bj-vjust  32786