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Theorem nfunidALT 34779
Description: Deduction version of nfuni 4580. (Contributed by NM, 19-Nov-2020.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nfunidALT.1 (𝜑𝑥𝐴)
Assertion
Ref Expression
nfunidALT (𝜑𝑥 𝐴)

Proof of Theorem nfunidALT
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 nfunidALT.1 . 2 (𝜑𝑥𝐴)
2 abidnf 3527 . . 3 (𝑥𝐴 → {𝑦 ∣ ∀𝑥 𝑦𝐴} = 𝐴)
32unieqd 4584 . 2 (𝑥𝐴 {𝑦 ∣ ∀𝑥 𝑦𝐴} = 𝐴)
4 nfaba1 2919 . . 3 𝑥{𝑦 ∣ ∀𝑥 𝑦𝐴}
54nfuni 4580 . 2 𝑥 {𝑦 ∣ ∀𝑥 𝑦𝐴}
61, 3, 5nfded 34776 1 (𝜑𝑥 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1629  wcel 2145  {cab 2757  wnfc 2900   cuni 4574
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-ral 3066  df-rex 3067  df-uni 4575
This theorem is referenced by: (None)
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