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Theorem nfreu 3432
Description: Bound-variable hypothesis builder for restricted unique existence. Usage of this theorem is discouraged because it depends on ax-13 2375. Use the weaker nfreuw 3412 when possible. (Contributed by NM, 30-Oct-2010.) (Revised by Mario Carneiro, 8-Oct-2016.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfrmo.1 𝑥𝐴
nfrmo.2 𝑥𝜑
Assertion
Ref Expression
nfreu 𝑥∃!𝑦𝐴 𝜑

Proof of Theorem nfreu
StepHypRef Expression
1 nftru 1801 . . 3 𝑦
2 nfrmo.1 . . . 4 𝑥𝐴
32a1i 11 . . 3 (⊤ → 𝑥𝐴)
4 nfrmo.2 . . . 4 𝑥𝜑
54a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
61, 3, 5nfreud 3430 . 2 (⊤ → Ⅎ𝑥∃!𝑦𝐴 𝜑)
76mptru 1544 1 𝑥∃!𝑦𝐴 𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1538  wnf 1780  wnfc 2888  ∃!wreu 3376
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-13 2375  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-nf 1781  df-mo 2538  df-eu 2567  df-cleq 2727  df-clel 2814  df-nfc 2890  df-reu 3379
This theorem is referenced by: (None)
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