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Theorem nfeu 2639
Description: Bound-variable hypothesis builder for the unique existential quantifier. Note that 𝑥 and 𝑦 need not be disjoint. (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 1786 . . 3 𝑦
2 nfeu.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfeud 2638 . 2 (⊤ → Ⅎ𝑥∃!𝑦𝜑)
54mptru 1529 1 𝑥∃!𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1523  wnf 1765  ∃!weu 2611
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992  ax-10 2112  ax-11 2126  ax-12 2141  ax-13 2344
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-tru 1525  df-ex 1762  df-nf 1766  df-mo 2576  df-eu 2612
This theorem is referenced by:  2eu7  2715  2eu8  2716  eusv2nf  5187  reusv2lem3  5192  bnj1489  31942  setrec2  44278
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