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Theorem nfii1 4300
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 4272 . 2  |-  |^|_ x  e.  A  B  =  { y  |  A. x  e.  A  y  e.  B }
2 nfra1 2785 . . 3  |-  F/ x A. x  e.  A  y  e.  B
32nfab 2616 . 2  |-  F/_ x { y  |  A. x  e.  A  y  e.  B }
41, 3nfcxfr 2610 1  |-  F/_ x |^|_ x  e.  A  B
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1904   {cab 2457   F/_wnfc 2599   A.wral 2756   |^|_ciin 4270
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451
This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-iin 4272
This theorem is referenced by:  dmiin  5084  scott0  8375  gruiin  9253  hspdifhsp  38556
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