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Theorem bj-hbsb3t 36495
Description: A theorem close to a closed form of hbsb3 2481. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-hbsb3t (∀𝑥(𝜑 → ∀𝑦𝜑) → ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑))

Proof of Theorem bj-hbsb3t
StepHypRef Expression
1 spsbim 2068 . 2 (∀𝑥(𝜑 → ∀𝑦𝜑) → ([𝑦 / 𝑥]𝜑 → [𝑦 / 𝑥]∀𝑦𝜑))
2 hbsb2a 2478 . 2 ([𝑦 / 𝑥]∀𝑦𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑)
31, 2syl6 35 1 (∀𝑥(𝜑 → ∀𝑦𝜑) → ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1532  [wsb 2060
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-10 2130  ax-12 2167  ax-13 2366
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-ex 1775  df-nf 1779  df-sb 2061
This theorem is referenced by:  bj-hbsb3  36496  bj-nfs1t  36497
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