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Theorem nfneg 8073
Description: Bound-variable hypothesis builder for the negative of a complex number. (Contributed by NM, 12-Jun-2005.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypothesis
Ref Expression
nfneg.1 𝑥𝐴
Assertion
Ref Expression
nfneg 𝑥-𝐴

Proof of Theorem nfneg
StepHypRef Expression
1 nfneg.1 . . . 4 𝑥𝐴
21a1i 9 . . 3 (⊤ → 𝑥𝐴)
32nfnegd 8072 . 2 (⊤ → 𝑥-𝐴)
43mptru 1344 1 𝑥-𝐴
Colors of variables: wff set class
Syntax hints:  wtru 1336  wnfc 2286  -cneg 8048
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rex 2441  df-v 2714  df-un 3106  df-sn 3566  df-pr 3567  df-op 3569  df-uni 3774  df-br 3967  df-iota 5136  df-fv 5179  df-ov 5828  df-neg 8050
This theorem is referenced by:  infssuzcldc  11842
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