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Theorem bj-stdpc4v 33089
Description: Version of stdpc4 2499 with a dv condition, which does not require ax-13 2408. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-stdpc4v (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem bj-stdpc4v
StepHypRef Expression
1 ax-1 6 . . 3 (𝜑 → (𝑥 = 𝑦𝜑))
21alimi 1887 . 2 (∀𝑥𝜑 → ∀𝑥(𝑥 = 𝑦𝜑))
3 bj-sb2v 33088 . 2 (∀𝑥(𝑥 = 𝑦𝜑) → [𝑦 / 𝑥]𝜑)
42, 3syl 17 1 (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1629  [wsb 2049
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-12 2203
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1853  df-sb 2050
This theorem is referenced by:  bj-2stdpc4v  33090  bj-sbftv  33098  bj-sbfvv  33100  bj-sbtv  33101  bj-vexwvt  33184  bj-ab0  33230
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