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Mirrors > Home > MPE Home > Th. List > tgcgrneq | Structured version Visualization version Unicode version |
Description: Congruence and equality. (Contributed by Thierry Arnoux, 27-Aug-2019.) |
Ref | Expression |
---|---|
tkgeom.p | |
tkgeom.d | |
tkgeom.i | Itv |
tkgeom.g | TarskiG |
tgcgrcomlr.a | |
tgcgrcomlr.b | |
tgcgrcomlr.c | |
tgcgrcomlr.d | |
tgcgrcomlr.6 | |
tgcgrneq.1 |
Ref | Expression |
---|---|
tgcgrneq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tgcgrneq.1 | . 2 | |
2 | tkgeom.p | . . . 4 | |
3 | tkgeom.d | . . . 4 | |
4 | tkgeom.i | . . . 4 Itv | |
5 | tkgeom.g | . . . 4 TarskiG | |
6 | tgcgrcomlr.a | . . . 4 | |
7 | tgcgrcomlr.b | . . . 4 | |
8 | tgcgrcomlr.c | . . . 4 | |
9 | tgcgrcomlr.d | . . . 4 | |
10 | tgcgrcomlr.6 | . . . 4 | |
11 | 2, 3, 4, 5, 6, 7, 8, 9, 10 | tgcgreqb 25376 | . . 3 |
12 | 11 | necon3bid 2838 | . 2 |
13 | 1, 12 | mpbid 222 | 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 |
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-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-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-iota 5851 df-fv 5896 df-ov 6653 df-trkgc 25347 df-trkg 25352 |
This theorem is referenced by: hlcgrex 25511 midexlem 25587 footex 25613 mideulem2 25626 opphllem3 25641 trgcopy 25696 iscgra1 25702 cgrane1 25704 cgrane2 25705 cgrcgra 25713 cgrg3col4 25734 tgsas2 25737 tgsas3 25738 tgasa1 25739 tgsss1 25741 |
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