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Theorem nfii1 5029
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 4994 . 2 𝑥𝐴 𝐵 = {𝑦 ∣ ∀𝑥𝐴 𝑦𝐵}
2 nfra1 3284 . . 3 𝑥𝑥𝐴 𝑦𝐵
32nfab 2911 . 2 𝑥{𝑦 ∣ ∀𝑥𝐴 𝑦𝐵}
41, 3nfcxfr 2903 1 𝑥 𝑥𝐴 𝐵
Colors of variables: wff setvar class
Syntax hints:  wcel 2108  {cab 2714  wnfc 2890  wral 3061   ciin 4992
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-ex 1780  df-nf 1784  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2892  df-ral 3062  df-iin 4994
This theorem is referenced by:  dmiin  5964  scott0  9926  gruiin  10850  zarclsiin  33870  iinssiin  45134  iooiinicc  45555  iooiinioc  45569  fnlimfvre  45689  fnlimabslt  45694  meaiininclem  46501  hspdifhsp  46631  smflimlem2  46787  smflim  46792  smflimmpt  46825  smfsuplem1  46826  smfsupmpt  46830  smfsupxr  46831  smfinflem  46832  smfinfmpt  46834  smflimsuplem7  46841  smflimsuplem8  46842  smflimsupmpt  46844  smfliminfmpt  46847  fsupdm  46857  finfdm  46861
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