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Mirrors > Home > MPE Home > Th. List > nfneg | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for the negative of a complex number. (Contributed by NM, 12-Jun-2005.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nfneg.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfneg | ⊢ Ⅎ𝑥-𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfneg.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
2 | 1 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
3 | 2 | nfnegd 10869 | . 2 ⊢ (⊤ → Ⅎ𝑥-𝐴) |
4 | 3 | mptru 1535 | 1 ⊢ Ⅎ𝑥-𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1529 Ⅎwnfc 2958 -cneg 10859 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-3an 1081 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ral 3140 df-rex 3141 df-rab 3144 df-v 3494 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-if 4464 df-sn 4558 df-pr 4560 df-op 4564 df-uni 4831 df-br 5058 df-iota 6307 df-fv 6356 df-ov 7148 df-neg 10861 |
This theorem is referenced by: riotaneg 11608 zriotaneg 12084 infcvgaux1i 15200 mbfposb 24181 dvfsum2 24558 infnsuprnmpt 41398 neglimc 41804 stoweidlem23 42185 stoweidlem47 42209 |
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