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Theorem nfeu 2485
Description: Bound-variable hypothesis builder for uniqueness. Note that 𝑥 and 𝑦 needn't be distinct. (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 7-Oct-2016.)
Hypothesis
Ref Expression
nfeu.1 𝑥𝜑
Assertion
Ref Expression
nfeu 𝑥∃!𝑦𝜑

Proof of Theorem nfeu
StepHypRef Expression
1 nftru 1727 . . 3 𝑦
2 nfeu.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfeud 2483 . 2 (⊤ → Ⅎ𝑥∃!𝑦𝜑)
54trud 1490 1 𝑥∃!𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1481  wnf 1705  ∃!weu 2469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-eu 2473
This theorem is referenced by:  2eu7  2558  2eu8  2559  eusv2nf  4824  reusv2lem3  4831  bnj1489  30829  setrec2  41732
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