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Theorem nfsb2 2358
Description: Bound-variable hypothesis builder for substitution. (Contributed by Mario Carneiro, 4-Oct-2016.)
Assertion
Ref Expression
nfsb2 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥[𝑦 / 𝑥]𝜑)

Proof of Theorem nfsb2
StepHypRef Expression
1 nfna1 2027 . 2 𝑥 ¬ ∀𝑥 𝑥 = 𝑦
2 hbsb2 2357 . 2 (¬ ∀𝑥 𝑥 = 𝑦 → ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑))
31, 2nf5d 2116 1 (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥[𝑦 / 𝑥]𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1479  wnf 1706  [wsb 1878
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-10 2017  ax-12 2045  ax-13 2244
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1703  df-nf 1708  df-sb 1879
This theorem is referenced by:  nfsb4t  2387  sbco3  2415  sb9  2424  wl-nfs1t  33295
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