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Mirrors > Home > ILE Home > Th. List > nfneg | 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 9 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
3 | 2 | nfnegd 8149 | . 2 ⊢ (⊤ → Ⅎ𝑥-𝐴) |
4 | 3 | mptru 1362 | 1 ⊢ Ⅎ𝑥-𝐴 |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1354 Ⅎwnfc 2306 -cneg 8125 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-v 2739 df-un 3133 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4003 df-iota 5177 df-fv 5223 df-ov 5875 df-neg 8127 |
This theorem is referenced by: infssuzcldc 11944 |
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