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Theorem nfxneg 45472
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 45452 . 2 (⊤ → 𝑥-𝑒𝐴)
43mptru 1547 1 𝑥-𝑒𝐴
Colors of variables: wff setvar class
Syntax hints:  wtru 1541  wnfc 2890  -𝑒cxne 13151
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2892  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-iota 6514  df-fv 6569  df-ov 7434  df-neg 11495  df-xneg 13154
This theorem is referenced by:  liminfvalxr  45798  xlimpnfxnegmnf  45829  liminfpnfuz  45831  xlimpnfxnegmnf2  45873
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