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Theorem nfunidALT 36282
 Description: Deduction version of nfuni 4807. (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 3642 . . 3 (𝑥𝐴 → {𝑦 ∣ ∀𝑥 𝑦𝐴} = 𝐴)
32unieqd 4814 . 2 (𝑥𝐴 {𝑦 ∣ ∀𝑥 𝑦𝐴} = 𝐴)
4 nfaba1 2963 . . 3 𝑥{𝑦 ∣ ∀𝑥 𝑦𝐴}
54nfuni 4807 . 2 𝑥 {𝑦 ∣ ∀𝑥 𝑦𝐴}
61, 3, 5nfded 36279 1 (𝜑𝑥 𝐴)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1536   ∈ wcel 2111  {cab 2776  Ⅎwnfc 2936  ∪ cuni 4800 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-ral 3111  df-rex 3112  df-v 3443  df-in 3888  df-ss 3898  df-uni 4801 This theorem is referenced by: (None)
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