Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > pautsetN | Structured version Visualization version Unicode version |
Description: The set of projective automorphisms. (Contributed by NM, 26-Jan-2012.) (New usage is discouraged.) |
Ref | Expression |
---|---|
pautset.s | |
pautset.m |
Ref | Expression |
---|---|
pautsetN |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 3212 | . 2 | |
2 | pautset.m | . . 3 | |
3 | fveq2 6191 | . . . . . . . . 9 | |
4 | pautset.s | . . . . . . . . 9 | |
5 | 3, 4 | syl6eqr 2674 | . . . . . . . 8 |
6 | f1oeq2 6128 | . . . . . . . 8 | |
7 | 5, 6 | syl 17 | . . . . . . 7 |
8 | f1oeq3 6129 | . . . . . . . 8 | |
9 | 5, 8 | syl 17 | . . . . . . 7 |
10 | 7, 9 | bitrd 268 | . . . . . 6 |
11 | 5 | raleqdv 3144 | . . . . . . 7 |
12 | 5, 11 | raleqbidv 3152 | . . . . . 6 |
13 | 10, 12 | anbi12d 747 | . . . . 5 |
14 | 13 | abbidv 2741 | . . . 4 |
15 | df-pautN 35277 | . . . 4 | |
16 | fvex 6201 | . . . . . . . . 9 | |
17 | 4, 16 | eqeltri 2697 | . . . . . . . 8 |
18 | 17, 17 | mapval 7869 | . . . . . . 7 |
19 | ovex 6678 | . . . . . . 7 | |
20 | 18, 19 | eqeltrri 2698 | . . . . . 6 |
21 | f1of 6137 | . . . . . . 7 | |
22 | 21 | ss2abi 3674 | . . . . . 6 |
23 | 20, 22 | ssexi 4803 | . . . . 5 |
24 | simpl 473 | . . . . . 6 | |
25 | 24 | ss2abi 3674 | . . . . 5 |
26 | 23, 25 | ssexi 4803 | . . . 4 |
27 | 14, 15, 26 | fvmpt 6282 | . . 3 |
28 | 2, 27 | syl5eq 2668 | . 2 |
29 | 1, 28 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 cab 2608 wral 2912 cvv 3200 wss 3574 wf 5884 wf1o 5887 cfv 5888 (class class class)co 6650 cmap 7857 cpsubsp 34782 cpautN 35273 |
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-8 1992 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-pow 4843 ax-pr 4906 ax-un 6949 |
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-mo 2475 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-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-map 7859 df-pautN 35277 |
This theorem is referenced by: ispautN 35385 |
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