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Theorem nfii1 3791
Description: Bound-variable hypothesis builder for indexed intersection. (Contributed by NM, 15-Oct-2003.)
Assertion
Ref Expression
nfii1 𝑥 𝑥𝐴 𝐵

Proof of Theorem nfii1
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 df-iin 3763 . 2 𝑥𝐴 𝐵 = {𝑦 ∣ ∀𝑥𝐴 𝑦𝐵}
2 nfra1 2425 . . 3 𝑥𝑥𝐴 𝑦𝐵
32nfab 2245 . 2 𝑥{𝑦 ∣ ∀𝑥𝐴 𝑦𝐵}
41, 3nfcxfr 2237 1 𝑥 𝑥𝐴 𝐵
Colors of variables: wff set class
Syntax hints:  wcel 1448  {cab 2086  wnfc 2227  wral 2375   ciin 3761
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082
This theorem depends on definitions:  df-bi 116  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-ral 2380  df-iin 3763
This theorem is referenced by:  dmiin  4723
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