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Theorem nfneg 7927
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 7926 . 2 (⊤ → 𝑥-𝐴)
43mptru 1325 1 𝑥-𝐴
Colors of variables: wff set class
Syntax hints:  wtru 1317  wnfc 2245  -cneg 7902
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-rex 2399  df-v 2662  df-un 3045  df-sn 3503  df-pr 3504  df-op 3506  df-uni 3707  df-br 3900  df-iota 5058  df-fv 5101  df-ov 5745  df-neg 7904
This theorem is referenced by:  infssuzcldc  11571
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