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Theorem nfeu 2655
Description: Bound-variable hypothesis builder for the unique existential quantifier. Note that 𝑥 and 𝑦 need not be disjoint. Usage of this theorem is discouraged because it depends on ax-13 2379. Use the weaker nfeuw 2654 when possible. (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 7-Oct-2016.) (New usage is discouraged.)
Hypothesis
Ref Expression
nfeu.1 𝑥𝜑
Assertion
Ref Expression
nfeu 𝑥∃!𝑦𝜑

Proof of Theorem nfeu
StepHypRef Expression
1 nftru 1806 . . 3 𝑦
2 nfeu.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfeud 2653 . 2 (⊤ → Ⅎ𝑥∃!𝑦𝜑)
54mptru 1545 1 𝑥∃!𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1539  wnf 1785  ∃!weu 2628
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2142  ax-11 2158  ax-12 2175  ax-13 2379
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-mo 2598  df-eu 2629
This theorem is referenced by:  2eu7  2720  2eu8  2721
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