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Theorem nfunidALT 37421
Description: Deduction version of nfuni 4871. (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 3659 . . 3 (𝑥𝐴 → {𝑦 ∣ ∀𝑥 𝑦𝐴} = 𝐴)
32unieqd 4878 . 2 (𝑥𝐴 {𝑦 ∣ ∀𝑥 𝑦𝐴} = 𝐴)
4 nfaba1 2914 . . 3 𝑥{𝑦 ∣ ∀𝑥 𝑦𝐴}
54nfuni 4871 . 2 𝑥 {𝑦 ∣ ∀𝑥 𝑦𝐴}
61, 3, 5nfded 37418 1 (𝜑𝑥 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1539  wcel 2106  {cab 2713  wnfc 2886   cuni 4864
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-nf 1786  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-nfc 2888  df-ral 3064  df-rex 3073  df-v 3446  df-in 3916  df-ss 3926  df-uni 4865
This theorem is referenced by: (None)
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