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Mirrors > Home > MPE Home > Th. List > tglinerflx2 | Structured version Visualization version Unicode version |
Description: Reflexivity law for line membership. Part of theorem 6.17 of [Schwabhauser] p. 45. (Contributed by Thierry Arnoux, 17-May-2019.) |
Ref | Expression |
---|---|
tglineelsb2.p | |
tglineelsb2.i | Itv |
tglineelsb2.l | LineG |
tglineelsb2.g | TarskiG |
tglineelsb2.1 | |
tglineelsb2.2 | |
tglineelsb2.4 |
Ref | Expression |
---|---|
tglinerflx2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tglineelsb2.p | . 2 | |
2 | tglineelsb2.i | . 2 Itv | |
3 | tglineelsb2.l | . 2 LineG | |
4 | tglineelsb2.g | . 2 TarskiG | |
5 | tglineelsb2.1 | . 2 | |
6 | tglineelsb2.2 | . 2 | |
7 | tglineelsb2.4 | . 2 | |
8 | eqid 2622 | . . 3 | |
9 | 1, 8, 2, 4, 5, 6 | tgbtwntriv2 25382 | . 2 |
10 | 1, 2, 3, 4, 5, 6, 6, 7, 9 | btwnlng1 25514 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 wne 2794 cfv 5888 (class class class)co 6650 cbs 15857 cds 15950 TarskiGcstrkg 25329 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-sep 4781 ax-nul 4789 ax-pr 4906 |
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-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 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-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-trkgc 25347 df-trkgcb 25349 df-trkg 25352 |
This theorem is referenced by: tghilberti1 25532 tglnpt2 25536 colline 25544 footex 25613 foot 25614 footne 25615 perprag 25618 colperpexlem3 25624 mideulem2 25626 opphllem 25627 opphllem5 25643 opphllem6 25644 opphl 25646 outpasch 25647 hlpasch 25648 lnopp2hpgb 25655 hypcgrlem1 25691 hypcgrlem2 25692 trgcopyeulem 25697 acopy 25724 acopyeu 25725 tgasa1 25739 |
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