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Theorem nfxneg 44717
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 44697 . 2 (⊤ → 𝑥-𝑒𝐴)
43mptru 1540 1 𝑥-𝑒𝐴
Colors of variables: wff setvar class
Syntax hints:  wtru 1534  wnfc 2875  -𝑒cxne 13090
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-nfc 2877  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-sn 4622  df-pr 4624  df-op 4628  df-uni 4901  df-br 5140  df-iota 6486  df-fv 6542  df-ov 7405  df-neg 11446  df-xneg 13093
This theorem is referenced by:  liminfvalxr  45045  xlimpnfxnegmnf  45076  liminfpnfuz  45078  xlimpnfxnegmnf2  45120
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