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Theorem nfreu 3295
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 1900 . . 3 𝑦
2 nfreu.1 . . . 4 𝑥𝐴
32a1i 11 . . 3 (⊤ → 𝑥𝐴)
4 nfreu.2 . . . 4 𝑥𝜑
54a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
61, 3, 5nfreud 3293 . 2 (⊤ → Ⅎ𝑥∃!𝑦𝐴 𝜑)
76mptru 1661 1 𝑥∃!𝑦𝐴 𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1654  wnf 1879  wnfc 2928  ∃!wreu 3091
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2377  ax-ext 2777
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-mo 2591  df-eu 2609  df-cleq 2792  df-clel 2795  df-nfc 2930  df-reu 3096
This theorem is referenced by:  sbcreu  3710  reuccats1OLD  13782  reuccatpfxs1  13817  2reu7  41968  2reu8  41969
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