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Theorem sbequ5 2534
Description: Substitution does not change an identical variable specifier. (Contributed by NM, 15-May-1993.)
Assertion
Ref Expression
sbequ5 ([𝑤 / 𝑧]∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥 𝑥 = 𝑦)

Proof of Theorem sbequ5
StepHypRef Expression
1 nfae 2468 . 2 𝑧𝑥 𝑥 = 𝑦
21sbf 2527 1 ([𝑤 / 𝑧]∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥 𝑥 = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wal 1629  [wsb 2049
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 835  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050
This theorem is referenced by: (None)
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