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Theorem nfun 3093
 Description: Bound-variable hypothesis builder for the union of classes. (Contributed by NM, 15-Sep-2003.) (Revised by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
nfun.1 xA
nfun.2 xB
Assertion
Ref Expression
nfun x(AB)

Proof of Theorem nfun
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 df-un 2916 . 2 (AB) = {y ∣ (y A y B)}
2 nfun.1 . . . . 5 xA
32nfcri 2169 . . . 4 x y A
4 nfun.2 . . . . 5 xB
54nfcri 2169 . . . 4 x y B
63, 5nfor 1463 . . 3 x(y A y B)
76nfab 2179 . 2 x{y ∣ (y A y B)}
81, 7nfcxfr 2172 1 x(AB)
 Colors of variables: wff set class Syntax hints:   ∨ wo 628   ∈ wcel 1390  {cab 2023  Ⅎwnfc 2162   ∪ cun 2909 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-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-un 2916 This theorem is referenced by:  nfsuc  4111
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