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Mirrors > Home > MPE Home > Th. List > tglng | Structured version Visualization version Unicode version |
Description: Lines of a Tarski Geometry. This relates to both Definition 4.10 of [Schwabhauser] p. 36. and Definition 6.14 of [Schwabhauser] p. 45. (Contributed by Thierry Arnoux, 28-Mar-2019.) |
Ref | Expression |
---|---|
tglng.p | |
tglng.l | LineG |
tglng.i | Itv |
Ref | Expression |
---|---|
tglng | TarskiG |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-trkg 25352 | . . . 4 TarskiG TarskiGC TarskiGB TarskiGCB Itv LineG | |
2 | inss2 3834 | . . . . 5 TarskiGC TarskiGB TarskiGCB Itv LineG TarskiGCB Itv LineG | |
3 | inss2 3834 | . . . . 5 TarskiGCB Itv LineG Itv LineG | |
4 | 2, 3 | sstri 3612 | . . . 4 TarskiGC TarskiGB TarskiGCB Itv LineG Itv LineG |
5 | 1, 4 | eqsstri 3635 | . . 3 TarskiG Itv LineG |
6 | 5 | sseli 3599 | . 2 TarskiG Itv LineG |
7 | tglng.l | . . 3 LineG | |
8 | tglng.p | . . . . 5 | |
9 | eqid 2622 | . . . . 5 | |
10 | tglng.i | . . . . 5 Itv | |
11 | 8, 9, 10 | istrkgl 25357 | . . . 4 Itv LineG LineG |
12 | 11 | simprbi 480 | . . 3 Itv LineG LineG |
13 | 7, 12 | syl5eq 2668 | . 2 Itv LineG |
14 | 6, 13 | syl 17 | 1 TarskiG |
Colors of variables: wff setvar class |
Syntax hints: wi 4 w3o 1036 wceq 1483 wcel 1990 cab 2608 crab 2916 cvv 3200 wsbc 3435 cdif 3571 cin 3573 csn 4177 cfv 5888 (class class class)co 6650 cmpt2 6652 cbs 15857 cds 15950 TarskiGcstrkg 25329 TarskiGCcstrkgc 25330 TarskiGBcstrkgb 25331 TarskiGCBcstrkgcb 25332 Itvcitv 25335 LineGclng 25336 |
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 ax-nul 4789 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-trkg 25352 |
This theorem is referenced by: tglnfn 25442 tglnunirn 25443 tglngval 25446 tgisline 25522 |
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