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Theorem bj-sbftv 32459
 Description: Version of sbft 2378 with a dv condition, which does not require ax-13 2245. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-sbftv (Ⅎ𝑥𝜑 → ([𝑦 / 𝑥]𝜑𝜑))
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem bj-sbftv
StepHypRef Expression
1 spsbe 1881 . . 3 ([𝑦 / 𝑥]𝜑 → ∃𝑥𝜑)
2 19.9t 2069 . . 3 (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))
31, 2syl5ib 234 . 2 (Ⅎ𝑥𝜑 → ([𝑦 / 𝑥]𝜑𝜑))
4 nf5r 2062 . . 3 (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑))
5 bj-stdpc4v 32450 . . 3 (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
64, 5syl6 35 . 2 (Ⅎ𝑥𝜑 → (𝜑 → [𝑦 / 𝑥]𝜑))
73, 6impbid 202 1 (Ⅎ𝑥𝜑 → ([𝑦 / 𝑥]𝜑𝜑))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196  ∀wal 1478  ∃wex 1701  Ⅎwnf 1705  [wsb 1877 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-12 2044 This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1702  df-nf 1707  df-sb 1878 This theorem is referenced by:  bj-sbfv  32460
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