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Mirrors > Home > MPE Home > Th. List > Mathboxes > polvalN | Structured version Visualization version Unicode version |
Description: Value of the projective subspace polarity function. (Contributed by NM, 23-Oct-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
polfval.o | |
polfval.a | |
polfval.m | |
polfval.p |
Ref | Expression |
---|---|
polvalN |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | polfval.a | . . . 4 | |
2 | fvex 6201 | . . . 4 | |
3 | 1, 2 | eqeltri 2697 | . . 3 |
4 | 3 | elpw2 4828 | . 2 |
5 | polfval.o | . . . . 5 | |
6 | polfval.m | . . . . 5 | |
7 | polfval.p | . . . . 5 | |
8 | 5, 1, 6, 7 | polfvalN 35190 | . . . 4 |
9 | 8 | fveq1d 6193 | . . 3 |
10 | iineq1 4535 | . . . . 5 | |
11 | 10 | ineq2d 3814 | . . . 4 |
12 | eqid 2622 | . . . 4 | |
13 | 3 | inex1 4799 | . . . 4 |
14 | 11, 12, 13 | fvmpt 6282 | . . 3 |
15 | 9, 14 | sylan9eq 2676 | . 2 |
16 | 4, 15 | sylan2br 493 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cvv 3200 cin 3573 wss 3574 cpw 4158 ciin 4521 cmpt 4729 cfv 5888 coc 15949 catm 34550 cpmap 34783 cpolN 35188 |
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-rep 4771 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 |
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-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 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-iun 4522 df-iin 4523 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-res 5126 df-ima 5127 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-polarityN 35189 |
This theorem is referenced by: polval2N 35192 pol0N 35195 polcon3N 35203 polatN 35217 |
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