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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 11451 | . 2 ⊢ (⊤ → Ⅎ𝑥-𝐴) |
4 | 3 | mptru 1548 | 1 ⊢ Ⅎ𝑥-𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1542 Ⅎwnfc 2883 -cneg 11441 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2703 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-clab 2710 df-cleq 2724 df-clel 2810 df-nfc 2885 df-ral 3062 df-rex 3071 df-rab 3433 df-v 3476 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4322 df-if 4528 df-sn 4628 df-pr 4630 df-op 4634 df-uni 4908 df-br 5148 df-iota 6492 df-fv 6548 df-ov 7408 df-neg 11443 |
This theorem is referenced by: riotaneg 12189 zriotaneg 12671 infcvgaux1i 15799 mbfposb 25161 dvfsum2 25542 infnsuprnmpt 43940 neglimc 44349 stoweidlem23 44725 stoweidlem47 44749 |
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