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Theorem bj-2stdpc4v 32395
Description: Version of 2stdpc4 2353 with a dv condition, which does not require ax-13 2245. (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 32394 . . 3 (∀𝑦𝜑 → [𝑤 / 𝑦]𝜑)
21alimi 1736 . 2 (∀𝑥𝑦𝜑 → ∀𝑥[𝑤 / 𝑦]𝜑)
3 bj-stdpc4v 32394 . 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 1478  [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-sb 1878
This theorem is referenced by: (None)
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