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Theorem nfunidALT 38971
Description: Deduction version of nfuni 4914. (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 3708 . . 3 (𝑥𝐴 → {𝑦 ∣ ∀𝑥 𝑦𝐴} = 𝐴)
32unieqd 4920 . 2 (𝑥𝐴 {𝑦 ∣ ∀𝑥 𝑦𝐴} = 𝐴)
4 nfaba1 2913 . . 3 𝑥{𝑦 ∣ ∀𝑥 𝑦𝐴}
54nfuni 4914 . 2 𝑥 {𝑦 ∣ ∀𝑥 𝑦𝐴}
61, 3, 5nfded 38968 1 (𝜑𝑥 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1538  wcel 2108  {cab 2714  wnfc 2890   cuni 4907
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-tru 1543  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-rex 3071  df-v 3482  df-ss 3968  df-uni 4908
This theorem is referenced by: (None)
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