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Theorem nfii1 4487
 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 4458 . 2 𝑥𝐴 𝐵 = {𝑦 ∣ ∀𝑥𝐴 𝑦𝐵}
2 nfra1 2925 . . 3 𝑥𝑥𝐴 𝑦𝐵
32nfab 2755 . 2 𝑥{𝑦 ∣ ∀𝑥𝐴 𝑦𝐵}
41, 3nfcxfr 2749 1 𝑥 𝑥𝐴 𝐵
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1977  {cab 2596  Ⅎwnfc 2738  ∀wral 2896  ∩ ciin 4456 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-iin 4458 This theorem is referenced by:  dmiin  5290  scott0  8632  gruiin  9511  iooiinicc  38616  iooiinioc  38630  fnlimfvre  38741  fnlimabslt  38746  meaiininclem  39376  hspdifhsp  39506  smflimlem2  39658  smflim  39663
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