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Theorem bj-stdpc4v 33187
Description: Version of stdpc4 2443 with a disjoint variable condition, which does not require ax-13 2352. (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 1906 . 2 (∀𝑥𝜑 → ∀𝑥(𝑥 = 𝑦𝜑))
3 sb2v 2283 . 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 1650  [wsb 2062
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-12 2211
This theorem depends on definitions:  df-bi 198  df-an 385  df-ex 1875  df-sb 2063
This theorem is referenced by:  bj-2stdpc4v  33188  bj-sbftv  33195  bj-sbfvv  33197  bj-sbtv  33198  bj-vexwvt  33280  bj-ab0  33327
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