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Theorem nfneg 8116
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 8115 . 2 (⊤ → 𝑥-𝐴)
43mptru 1357 1 𝑥-𝐴
Colors of variables: wff set class
Syntax hints:  wtru 1349  wnfc 2299  -cneg 8091
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rex 2454  df-v 2732  df-un 3125  df-sn 3589  df-pr 3590  df-op 3592  df-uni 3797  df-br 3990  df-iota 5160  df-fv 5206  df-ov 5856  df-neg 8093
This theorem is referenced by:  infssuzcldc  11906
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