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Theorem bj-nfs1t2 32354
Description: A theorem close to a closed form of nfs1 2364. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-nfs1t2 (∀𝑥𝑦𝜑 → Ⅎ𝑥[𝑦 / 𝑥]𝜑)

Proof of Theorem bj-nfs1t2
StepHypRef Expression
1 nf5r 2062 . . 3 (Ⅎ𝑦𝜑 → (𝜑 → ∀𝑦𝜑))
21alimi 1736 . 2 (∀𝑥𝑦𝜑 → ∀𝑥(𝜑 → ∀𝑦𝜑))
3 bj-nfs1t 32353 . 2 (∀𝑥(𝜑 → ∀𝑦𝜑) → Ⅎ𝑥[𝑦 / 𝑥]𝜑)
42, 3syl 17 1 (∀𝑥𝑦𝜑 → Ⅎ𝑥[𝑦 / 𝑥]𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478  wnf 1705  [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-10 2016  ax-12 2044  ax-13 2245
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1702  df-nf 1707  df-sb 1878
This theorem is referenced by:  bj-nfs1  32355
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