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Theorem nfii1 3851
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 3823 . 2 𝑥𝐴 𝐵 = {𝑦 ∣ ∀𝑥𝐴 𝑦𝐵}
2 nfra1 2469 . . 3 𝑥𝑥𝐴 𝑦𝐵
32nfab 2287 . 2 𝑥{𝑦 ∣ ∀𝑥𝐴 𝑦𝐵}
41, 3nfcxfr 2279 1 𝑥 𝑥𝐴 𝐵
Colors of variables: wff set class
Syntax hints:  wcel 1481  {cab 2126  wnfc 2269  wral 2417   ciin 3821
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-iin 3823
This theorem is referenced by:  dmiin  4792
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