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Theorem nfsb2 2482
Description: Bound-variable hypothesis builder for substitution. Usage of this theorem is discouraged because it depends on ax-13 2371. (Contributed by Mario Carneiro, 4-Oct-2016.) (New usage is discouraged.)
Assertion
Ref Expression
nfsb2 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥[𝑦 / 𝑥]𝜑)

Proof of Theorem nfsb2
StepHypRef Expression
1 nfna1 2150 . 2 𝑥 ¬ ∀𝑥 𝑥 = 𝑦
2 hbsb2 2481 . 2 (¬ ∀𝑥 𝑥 = 𝑦 → ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑))
31, 2nf5d 2281 1 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥[𝑦 / 𝑥]𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1540  wnf 1786  [wsb 2068
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-10 2138  ax-12 2172  ax-13 2371
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-ex 1783  df-nf 1787  df-sb 2069
This theorem is referenced by:  nfsb4t  2498  sbco3  2512  sb9  2518  wl-nfs1t  36042
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