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Theorem nfsbvOLD 2351
 Description: Obsolete version of nfsbv 2350 as of 13-Aug-2023. (Contributed by Wolf Lammen, 7-Feb-2023.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nfsbv.nf 𝑧𝜑
Assertion
Ref Expression
nfsbvOLD 𝑧[𝑦 / 𝑥]𝜑
Distinct variable group:   𝑥,𝑧,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦,𝑧)

Proof of Theorem nfsbvOLD
StepHypRef Expression
1 sb6 2094 . 2 ([𝑦 / 𝑥]𝜑 ↔ ∀𝑥(𝑥 = 𝑦𝜑))
2 nfv 1916 . . . 4 𝑧 𝑥 = 𝑦
3 nfsbv.nf . . . 4 𝑧𝜑
42, 3nfim 1898 . . 3 𝑧(𝑥 = 𝑦𝜑)
54nfal 2343 . 2 𝑧𝑥(𝑥 = 𝑦𝜑)
61, 5nfxfr 1854 1 𝑧[𝑦 / 𝑥]𝜑
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1536  Ⅎwnf 1785  [wsb 2070 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-10 2146  ax-11 2162  ax-12 2178 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-nf 1786  df-sb 2071 This theorem is referenced by: (None)
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