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Theorem nfuni 3897
 Description: Bound-variable hypothesis builder for union. (Contributed by NM, 30-Dec-1996.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Hypothesis
Ref Expression
nfuni.1 xA
Assertion
Ref Expression
nfuni xA

Proof of Theorem nfuni
Dummy variables y z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dfuni2 3893 . 2 A = {y z A y z}
2 nfuni.1 . . . 4 xA
3 nfv 1619 . . . 4 x y z
42, 3nfrex 2669 . . 3 xz A y z
54nfab 2493 . 2 x{y z A y z}
61, 5nfcxfr 2486 1 xA
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1710  {cab 2339  Ⅎwnfc 2476  ∃wrex 2615  ∪cuni 3891 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-uni 3892 This theorem is referenced by:  nfiota1  4341
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