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Theorem nfeuw 2678
Description: Bound-variable hypothesis builder for the unique existential quantifier. Version of nfeu 2679 with a disjoint variable condition, which does not require ax-13 2390. (Contributed by NM, 8-Mar-1995.) (Revised by Gino Giotto, 10-Jan-2024.)
Hypothesis
Ref Expression
nfeuw.1 𝑥𝜑
Assertion
Ref Expression
nfeuw 𝑥∃!𝑦𝜑
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem nfeuw
StepHypRef Expression
1 nftru 1805 . . 3 𝑦
2 nfeuw.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfeudw 2676 . 2 (⊤ → Ⅎ𝑥∃!𝑦𝜑)
54mptru 1544 1 𝑥∃!𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1538  wnf 1784  ∃!weu 2652
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2145  ax-11 2161  ax-12 2177
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-mo 2622  df-eu 2653
This theorem is referenced by:  eusv2nf  5272  reusv2lem3  5277  bnj1489  32336  setrec2  44985
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