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 41708 | . 2 ⊢ (⊤ → Ⅎ𝑥-𝑒𝐴) |
4 | 3 | mptru 1540 | 1 ⊢ Ⅎ𝑥-𝑒𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1534 Ⅎwnfc 2961 -𝑒cxne 12498 |
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 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-rex 3144 df-rab 3147 df-v 3496 df-dif 3938 df-un 3940 df-in 3942 df-ss 3951 df-nul 4291 df-if 4467 df-sn 4561 df-pr 4563 df-op 4567 df-uni 4832 df-br 5059 df-iota 6308 df-fv 6357 df-ov 7153 df-neg 10867 df-xneg 12501 |
This theorem is referenced by: liminfvalxr 42057 xlimpnfxnegmnf 42088 liminfpnfuz 42090 xlimpnfxnegmnf2 42132 |
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