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Theorem bj-nfs1t2 33317
Description: A theorem close to a closed form of nfs1 2440. (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 2177 . . 3 (Ⅎ𝑦𝜑 → (𝜑 → ∀𝑦𝜑))
21alimi 1855 . 2 (∀𝑥𝑦𝜑 → ∀𝑥(𝜑 → ∀𝑦𝜑))
3 bj-nfs1t 33316 . 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 1599  wnf 1827  [wsb 2011
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2054  ax-10 2134  ax-12 2162  ax-13 2333
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-ex 1824  df-nf 1828  df-sb 2012
This theorem is referenced by:  bj-nfs1  33318
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