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Theorem sb8fOLD 2344
Description: Obsolete version of sb8f 2343 as of 5-Dec-2024. (Contributed by NM, 16-May-1993.) (Revised by Wolf Lammen, 19-Jan-2023.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
sb8f.nf 𝑦𝜑
Assertion
Ref Expression
sb8fOLD (∀𝑥𝜑 ↔ ∀𝑦[𝑦 / 𝑥]𝜑)
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem sb8fOLD
StepHypRef Expression
1 sb8f.nf . 2 𝑦𝜑
2 nfs1v 2145 . 2 𝑥[𝑦 / 𝑥]𝜑
3 sbequ12 2235 . 2 (𝑥 = 𝑦 → (𝜑 ↔ [𝑦 / 𝑥]𝜑))
41, 2, 3cbvalv1 2331 1 (∀𝑥𝜑 ↔ ∀𝑦[𝑦 / 𝑥]𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 205  wal 1531  wnf 1777  [wsb 2059
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-10 2129  ax-11 2146  ax-12 2163
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-ex 1774  df-nf 1778  df-sb 2060
This theorem is referenced by: (None)
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