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Theorem nfeuw 2592
Description: Bound-variable hypothesis builder for the unique existential quantifier. Version of nfeu 2593 with a disjoint variable condition, which does not require ax-13 2376. (Contributed by NM, 8-Mar-1995.) Avoid ax-13 2376. (Revised by GG, 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 1803 . . 3 𝑦
2 nfeuw.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfeudw 2590 . 2 (⊤ → Ⅎ𝑥∃!𝑦𝜑)
54mptru 1546 1 𝑥∃!𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1540  wnf 1782  ∃!weu 2567
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-10 2140  ax-11 2156  ax-12 2176
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-ex 1779  df-nf 1783  df-mo 2539  df-eu 2568
This theorem is referenced by:  nfreuw  3413  eusv2nf  5394  reusv2lem3  5399  bnj1489  35071  setrec2  49269
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