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Theorem nfiinya 3660
 Description: Bound-variable hypothesis builder for indexed intersection. (Contributed by Mario Carneiro, 25-Jan-2014.)
Hypotheses
Ref Expression
nfiunya.1 yA
nfiunya.2 yB
Assertion
Ref Expression
nfiinya y x A B
Distinct variable group:   x,A
Allowed substitution hints:   A(y)   B(x,y)

Proof of Theorem nfiinya
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 df-iin 3634 . 2 x A B = {zx A z B}
2 nfiunya.1 . . . 4 yA
3 nfiunya.2 . . . . 5 yB
43nfcri 2154 . . . 4 y z B
52, 4nfralya 2340 . . 3 yx A z B
65nfab 2164 . 2 y{zx A z B}
71, 6nfcxfr 2157 1 y x A B
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1374  {cab 2008  Ⅎwnfc 2147  ∀wral 2284  ∩ ciin 3632 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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004 This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-ral 2289  df-iin 3634 This theorem is referenced by: (None)
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