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Theorem nfsb2 2518
 Description: Bound-variable hypothesis builder for substitution. Usage of this theorem is discouraged because it depends on ax-13 2386. (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 2152 . 2 𝑥 ¬ ∀𝑥 𝑥 = 𝑦
2 hbsb2 2517 . 2 (¬ ∀𝑥 𝑥 = 𝑦 → ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑))
31, 2nf5d 2288 1 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥[𝑦 / 𝑥]𝜑)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1531  Ⅎwnf 1780  [wsb 2065 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 1907  ax-6 1966  ax-7 2011  ax-10 2141  ax-12 2172  ax-13 2386 This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-ex 1777  df-nf 1781  df-sb 2066 This theorem is referenced by:  nfsb4t  2535  sbco3  2551  sb9  2557  wl-nfs1t  34771
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