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Theorem bj-2stdpc4v 31943
Description: Version of 2stdpc4 2342 with a dv condition, which does not require ax-13 2234. (Contributed by BJ, 24-Jun-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-2stdpc4v (∀𝑥𝑦𝜑 → [𝑧 / 𝑥][𝑤 / 𝑦]𝜑)
Distinct variable groups:   𝑥,𝑧   𝑦,𝑤
Allowed substitution hints:   𝜑(𝑥,𝑦,𝑧,𝑤)

Proof of Theorem bj-2stdpc4v
StepHypRef Expression
1 bj-stdpc4v 31942 . . 3 (∀𝑦𝜑 → [𝑤 / 𝑦]𝜑)
21alimi 1730 . 2 (∀𝑥𝑦𝜑 → ∀𝑥[𝑤 / 𝑦]𝜑)
3 bj-stdpc4v 31942 . 2 (∀𝑥[𝑤 / 𝑦]𝜑 → [𝑧 / 𝑥][𝑤 / 𝑦]𝜑)
42, 3syl 17 1 (∀𝑥𝑦𝜑 → [𝑧 / 𝑥][𝑤 / 𝑦]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: (None)
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