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Theorem bj-stdpc4v 31942
 Description: Version of stdpc4 2341 with a dv condition, which does not require ax-13 2234. (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 1730 . 2 (∀𝑥𝜑 → ∀𝑥(𝑥 = 𝑦𝜑))
3 bj-sb2v 31941 . 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 1473  [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-sb 1868 This theorem is referenced by:  bj-2stdpc4v  31943  bj-sbftv  31951  bj-sbfvv  31953  bj-sbtv  31954  bj-vexwvt  32050  bj-ab0  32094
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