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Theorem nfreu 3093
 Description: Bound-variable hypothesis builder for restricted unique existence. (Contributed by NM, 30-Oct-2010.) (Revised by Mario Carneiro, 8-Oct-2016.)
Hypotheses
Ref Expression
nfreu.1 𝑥𝐴
nfreu.2 𝑥𝜑
Assertion
Ref Expression
nfreu 𝑥∃!𝑦𝐴 𝜑

Proof of Theorem nfreu
StepHypRef Expression
1 nftru 1721 . . 3 𝑦
2 nfreu.1 . . . 4 𝑥𝐴
32a1i 11 . . 3 (⊤ → 𝑥𝐴)
4 nfreu.2 . . . 4 𝑥𝜑
54a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
61, 3, 5nfreud 3091 . 2 (⊤ → Ⅎ𝑥∃!𝑦𝐴 𝜑)
76trud 1484 1 𝑥∃!𝑦𝐴 𝜑
 Colors of variables: wff setvar class Syntax hints:  ⊤wtru 1476  Ⅎwnf 1699  Ⅎwnfc 2738  ∃!wreu 2898 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-eu 2462  df-cleq 2603  df-clel 2606  df-nfc 2740  df-reu 2903 This theorem is referenced by:  sbcreu  3482  2reu7  39840  2reu8  39841
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