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Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > nfxneg | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for the negative of an extended real number. (Contributed by Glauco Siliprandi, 2-Jan-2022.) |
Ref | Expression |
---|---|
nfxneg.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfxneg | ⊢ Ⅎ𝑥-𝑒𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfxneg.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
2 | 1 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
3 | 2 | nfxnegd 45391 | . 2 ⊢ (⊤ → Ⅎ𝑥-𝑒𝐴) |
4 | 3 | mptru 1544 | 1 ⊢ Ⅎ𝑥-𝑒𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1538 Ⅎwnfc 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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