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Theorem nfii1 3934
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 3908 . 2  |-  |^|_ x  e.  A  B  =  { y  |  A. x  e.  A  y  e.  B }
2 nfra1 2593 . . 3  |-  F/ x A. x  e.  A  y  e.  B
32nfab 2423 . 2  |-  F/_ x { y  |  A. x  e.  A  y  e.  B }
41, 3nfcxfr 2416 1  |-  F/_ x |^|_ x  e.  A  B
Colors of variables: wff set class
Syntax hints:    e. wcel 1684   {cab 2269   F/_wnfc 2406   A.wral 2543   |^|_ciin 3906
This theorem is referenced by:  dmiin  4922  scott0  7556  gruiin  8432
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-iin 3908
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