| 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 45452 | . 2 ⊢ (⊤ → Ⅎ𝑥-𝑒𝐴) |
| 4 | 3 | mptru 1547 | 1 ⊢ Ⅎ𝑥-𝑒𝐴 |
| Colors of variables: wff setvar class |
| Syntax hints: ⊤wtru 1541 Ⅎwnfc 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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