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Theorem nfreu 3306
Description: Bound-variable hypothesis builder for restricted unique existence. Usage of this theorem is discouraged because it depends on ax-13 2372. Use the weaker nfreuw 3303 when possible. (Contributed by NM, 30-Oct-2010.) (Revised by Mario Carneiro, 8-Oct-2016.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfreu.1 𝑥𝐴
nfreu.2 𝑥𝜑
Assertion
Ref Expression
nfreu 𝑥∃!𝑦𝐴 𝜑

Proof of Theorem nfreu
StepHypRef Expression
1 nftru 1807 . . 3 𝑦
2 nfreu.1 . . . 4 𝑥𝐴
32a1i 11 . . 3 (⊤ → 𝑥𝐴)
4 nfreu.2 . . . 4 𝑥𝜑
54a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
61, 3, 5nfreud 3300 . 2 (⊤ → Ⅎ𝑥∃!𝑦𝐴 𝜑)
76mptru 1546 1 𝑥∃!𝑦𝐴 𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1540  wnf 1786  wnfc 2887  ∃!wreu 3066
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-13 2372  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-ex 1783  df-nf 1787  df-mo 2540  df-eu 2569  df-cleq 2730  df-clel 2816  df-nfc 2889  df-reu 3071
This theorem is referenced by: (None)
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