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Theorem nfreu 3252
Description: Bound-variable hypothesis builder for restricted unique existence. (Contributed by NM, 30-Oct-2010.) (Revised by Mario Carneiro, 8-Oct-2016.)
Hypotheses
Ref Expression
nfreu.1 𝑥𝐴
nfreu.2 𝑥𝜑
Assertion
Ref Expression
nfreu 𝑥∃!𝑦𝐴 𝜑

Proof of Theorem nfreu
StepHypRef Expression
1 nftru 1879 . . 3 𝑦
2 nfreu.1 . . . 4 𝑥𝐴
32a1i 11 . . 3 (⊤ → 𝑥𝐴)
4 nfreu.2 . . . 4 𝑥𝜑
54a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
61, 3, 5nfreud 3250 . 2 (⊤ → Ⅎ𝑥∃!𝑦𝐴 𝜑)
76trud 1642 1 𝑥∃!𝑦𝐴 𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1633  wnf 1857  wnfc 2889  ∃!wreu 3052
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-eu 2611  df-cleq 2753  df-clel 2756  df-nfc 2891  df-reu 3057
This theorem is referenced by:  sbcreu  3656  reuccats1  13680  2reu7  41697  2reu8  41698
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