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Theorem nfii1 3729
Description: Bound-variable hypothesis builder for indexed intersection. (Contributed by NM, 15-Oct-2003.)
Assertion
Ref Expression
nfii1  |-  F/_ x |^|_ x  e.  A  B

Proof of Theorem nfii1
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 df-iin 3701 . 2  |-  |^|_ x  e.  A  B  =  { y  |  A. x  e.  A  y  e.  B }
2 nfra1 2402 . . 3  |-  F/ x A. x  e.  A  y  e.  B
32nfab 2227 . 2  |-  F/_ x { y  |  A. x  e.  A  y  e.  B }
41, 3nfcxfr 2220 1  |-  F/_ x |^|_ x  e.  A  B
Colors of variables: wff set class
Syntax hints:    e. wcel 1434   {cab 2069   F/_wnfc 2210   A.wral 2353   |^|_ciin 3699
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-iin 3701
This theorem is referenced by:  dmiin  4628
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