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 41722 | . 2 ⊢ (⊤ → Ⅎ𝑥-𝑒𝐴) |
4 | 3 | mptru 1544 | 1 ⊢ Ⅎ𝑥-𝑒𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1538 Ⅎwnfc 2963 -𝑒cxne 12507 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-ral 3145 df-rex 3146 df-rab 3149 df-v 3498 df-dif 3941 df-un 3943 df-in 3945 df-ss 3954 df-nul 4294 df-if 4470 df-sn 4570 df-pr 4572 df-op 4576 df-uni 4841 df-br 5069 df-iota 6316 df-fv 6365 df-ov 7161 df-neg 10875 df-xneg 12510 |
This theorem is referenced by: liminfvalxr 42071 xlimpnfxnegmnf 42102 liminfpnfuz 42104 xlimpnfxnegmnf2 42146 |
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