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Theorem wl-nfsbtv 37558
Description: Closed form of nfsbv 2329. (Contributed by Wolf Lammen, 2-May-2025.)
Assertion
Ref Expression
wl-nfsbtv (∀𝑥𝑧𝜑 → Ⅎ𝑧[𝑦 / 𝑥]𝜑)
Distinct variable groups:   𝑥,𝑧   𝑦,𝑧
Allowed substitution hints:   𝜑(𝑥,𝑦,𝑧)

Proof of Theorem wl-nfsbtv
StepHypRef Expression
1 stdpc4 2066 . 2 (∀𝑥𝑧𝜑 → [𝑦 / 𝑥]Ⅎ𝑧𝜑)
2 sbnf 2311 . 2 ([𝑦 / 𝑥]Ⅎ𝑧𝜑 ↔ Ⅎ𝑧[𝑦 / 𝑥]𝜑)
31, 2sylib 218 1 (∀𝑥𝑧𝜑 → Ⅎ𝑧[𝑦 / 𝑥]𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1535  wnf 1780  [wsb 2062
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-10 2139  ax-11 2155  ax-12 2175
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-nf 1781  df-sb 2063
This theorem is referenced by:  wl-sb8eutv  37560
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