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Theorem bj-sbfv 31952
Description: Version of sbf 2368 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-sbfv.1 𝑥𝜑
Assertion
Ref Expression
bj-sbfv ([𝑦 / 𝑥]𝜑𝜑)
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem bj-sbfv
StepHypRef Expression
1 bj-sbfv.1 . 2 𝑥𝜑
2 bj-sbftv 31951 . 2 (Ⅎ𝑥𝜑 → ([𝑦 / 𝑥]𝜑𝜑))
31, 2ax-mp 5 1 ([𝑦 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 195  wnf 1699  [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-nf 1701  df-sb 1868
This theorem is referenced by: (None)
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