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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 10155 | . 2 ⊢ (⊤ → Ⅎ𝑥-𝐴) |
4 | 3 | trud 1484 | 1 ⊢ Ⅎ𝑥-𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1476 Ⅎwnfc 2738 -cneg 10146 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ral 2901 df-rex 2902 df-rab 2905 df-v 3175 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-sn 4126 df-pr 4128 df-op 4132 df-uni 4373 df-br 4584 df-iota 5768 df-fv 5812 df-ov 6552 df-neg 10148 |
This theorem is referenced by: riotaneg 10879 zriotaneg 11367 infcvgaux1i 14428 mbfposb 23226 dvfsum2 23601 neglimc 38714 stoweidlem23 38916 stoweidlem47 38940 |
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