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Theorem nfxneg 45411
Description: Bound-variable hypothesis builder for the negative of an extended real number. (Contributed by Glauco Siliprandi, 2-Jan-2022.)
Hypothesis
Ref Expression
nfxneg.1 𝑥𝐴
Assertion
Ref Expression
nfxneg 𝑥-𝑒𝐴

Proof of Theorem nfxneg
StepHypRef Expression
1 nfxneg.1 . . . 4 𝑥𝐴
21a1i 11 . . 3 (⊤ → 𝑥𝐴)
32nfxnegd 45391 . 2 (⊤ → 𝑥-𝑒𝐴)
43mptru 1544 1 𝑥-𝑒𝐴
Colors of variables: wff setvar class
Syntax hints:  wtru 1538  wnfc 2888  -𝑒cxne 13149
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-nf 1781  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-ral 3060  df-rex 3069  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-iota 6516  df-fv 6571  df-ov 7434  df-neg 11493  df-xneg 13152
This theorem is referenced by:  liminfvalxr  45739  xlimpnfxnegmnf  45770  liminfpnfuz  45772  xlimpnfxnegmnf2  45814
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