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Theorem nfxneg 43703
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 43683 . 2 (⊤ → 𝑥-𝑒𝐴)
43mptru 1549 1 𝑥-𝑒𝐴
Colors of variables: wff setvar class
Syntax hints:  wtru 1543  wnfc 2888  -𝑒cxne 13031
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-nfc 2890  df-ral 3066  df-rex 3075  df-rab 3409  df-v 3448  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-uni 4867  df-br 5107  df-iota 6449  df-fv 6505  df-ov 7361  df-neg 11389  df-xneg 13034
This theorem is referenced by:  liminfvalxr  44031  xlimpnfxnegmnf  44062  liminfpnfuz  44064  xlimpnfxnegmnf2  44106
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