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Mirrors > Home > MPE Home > Th. List > Mathboxes > nnssi2 | Structured version Visualization version Unicode version |
Description: Convert a theorem for real/complex numbers into one for positive integers. (Contributed by Jeff Hoffman, 17-Jun-2008.) |
Ref | Expression |
---|---|
nnssi2.1 | |
nnssi2.2 | |
nnssi2.3 |
Ref | Expression |
---|---|
nnssi2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnssi2.1 | . . . . 5 | |
2 | 1 | sseli 3599 | . . . 4 |
3 | 1 | sseli 3599 | . . . 4 |
4 | nnssi2.2 | . . . 4 | |
5 | 2, 3, 4 | 3anim123i 1247 | . . 3 |
6 | 5 | 3anidm23 1385 | . 2 |
7 | nnssi2.3 | . 2 | |
8 | 6, 7 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wcel 1990 wss 3574 cn 11020 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-in 3581 df-ss 3588 |
This theorem is referenced by: nndivsub 32456 |
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