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Theorem hbab1 2011
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
hbab1 (y {xφ} → x y {xφ})
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)

Proof of Theorem hbab1
StepHypRef Expression
1 df-clab 2009 . 2 (y {xφ} ↔ [y / x]φ)
2 hbs1 1796 . 2 ([y / x]φx[y / x]φ)
31, 2hbxfrbi 1341 1 (y {xφ} → x y {xφ})
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1226   wcel 1374  [wsb 1627  {cab 2008
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-5 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-11 1378  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409
This theorem depends on definitions:  df-bi 110  df-sb 1628  df-clab 2009
This theorem is referenced by:  nfsab1  2012  abeq2  2128
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