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Theorem nfiu1OLD 5054
Description: Obsolete version of nfiu1 5053 as of 14-May-2025. (Contributed by NM, 12-Oct-2003.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nfiu1OLD 𝑥 𝑥𝐴 𝐵

Proof of Theorem nfiu1OLD
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 df-iun 5021 . 2 𝑥𝐴 𝐵 = {𝑦 ∣ ∃𝑥𝐴 𝑦𝐵}
2 nfre1 3286 . . 3 𝑥𝑥𝐴 𝑦𝐵
32nfab 2910 . 2 𝑥{𝑦 ∣ ∃𝑥𝐴 𝑦𝐵}
41, 3nfcxfr 2902 1 𝑥 𝑥𝐴 𝐵
Colors of variables: wff setvar class
Syntax hints:  wcel 2103  {cab 2711  wnfc 2888  wrex 3072   ciun 5019
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2105  ax-9 2113  ax-10 2136  ax-11 2153  ax-12 2173  ax-ext 2705
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1778  df-nf 1782  df-sb 2065  df-clab 2712  df-cleq 2726  df-clel 2813  df-nfc 2890  df-rex 3073  df-iun 5021
This theorem is referenced by: (None)
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