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Theorem nfsb4or 1896
Description: A variable not free remains so after substitution with a distinct variable. (Contributed by Jim Kingdon, 11-May-2018.)
Hypothesis
Ref Expression
nfsb4or.1 zφ
Assertion
Ref Expression
nfsb4or (z z = y z[y / x]φ)

Proof of Theorem nfsb4or
Dummy variable w is distinct from all other variables.
StepHypRef Expression
1 nfsb4or.1 . . 3 zφ
21nfsb 1819 . 2 z[w / x]φ
3 sbequ 1718 . 2 (w = y → ([w / x]φ ↔ [y / x]φ))
42, 3dvelimor 1891 1 (z z = y z[y / x]φ)
Colors of variables: wff set class
Syntax hints:   wo 628  wal 1240  wnf 1346  [wsb 1642
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643
This theorem is referenced by: (None)
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