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Theorem nfunidALT 33073
Description: Deduction version of nfuni 4367. (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 3336 . . 3 (𝑥𝐴 → {𝑦 ∣ ∀𝑥 𝑦𝐴} = 𝐴)
32unieqd 4371 . 2 (𝑥𝐴 {𝑦 ∣ ∀𝑥 𝑦𝐴} = 𝐴)
4 nfaba1 2750 . . 3 𝑥{𝑦 ∣ ∀𝑥 𝑦𝐴}
54nfuni 4367 . 2 𝑥 {𝑦 ∣ ∀𝑥 𝑦𝐴}
61, 3, 5nfded 33070 1 (𝜑𝑥 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1472  wcel 1975  {cab 2590  wnfc 2732   cuni 4361
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-10 2004  ax-11 2019  ax-12 2031  ax-13 2227  ax-ext 2584
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1866  df-clab 2591  df-cleq 2597  df-clel 2600  df-nfc 2734  df-ral 2895  df-rex 2896  df-uni 4362
This theorem is referenced by: (None)
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