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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > mapprop | Structured version Unicode version |
Description: An unordered pair containing two ordered pairs as an element of the mapping operation. (Contributed by AV, 16-Apr-2019.) |
Ref | Expression |
---|---|
mapprop.f |
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Ref | Expression |
---|---|
mapprop |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 457 |
. . . . . . 7
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2 | simpl 457 |
. . . . . . 7
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3 | 1, 2 | anim12i 566 |
. . . . . 6
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4 | 3 | 3adant3 1008 |
. . . . 5
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5 | simpr 461 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | simpr 461 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 5, 6 | anim12i 566 |
. . . . . 6
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8 | 7 | 3adant3 1008 |
. . . . 5
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9 | simpl 457 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 9 | 3ad2ant3 1011 |
. . . . 5
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11 | fprg 6003 |
. . . . 5
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12 | 4, 8, 10, 11 | syl3anc 1219 |
. . . 4
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13 | mapprop.f |
. . . . 5
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14 | 13 | feq1i 5662 |
. . . 4
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15 | 12, 14 | sylibr 212 |
. . 3
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16 | prssi 4140 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | 7, 16 | syl 16 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 17 | 3adant3 1008 |
. . 3
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19 | fss 5678 |
. . 3
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20 | 15, 18, 19 | syl2anc 661 |
. 2
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21 | simpr 461 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
22 | 21 | 3ad2ant3 1011 |
. . 3
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23 | prex 4645 |
. . 3
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24 | elmapg 7340 |
. . 3
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25 | 22, 23, 24 | sylancl 662 |
. 2
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26 | 20, 25 | mpbird 232 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 ax-sep 4524 ax-nul 4532 ax-pow 4581 ax-pr 4642 ax-un 6485 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2266 df-mo 2267 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ne 2650 df-ral 2804 df-rex 2805 df-rab 2808 df-v 3080 df-sbc 3295 df-dif 3442 df-un 3444 df-in 3446 df-ss 3453 df-nul 3749 df-if 3903 df-pw 3973 df-sn 3989 df-pr 3991 df-op 3995 df-uni 4203 df-br 4404 df-opab 4462 df-id 4747 df-xp 4957 df-rel 4958 df-cnv 4959 df-co 4960 df-dm 4961 df-rn 4962 df-iota 5492 df-fun 5531 df-fn 5532 df-f 5533 df-fv 5537 df-ov 6206 df-oprab 6207 df-mpt2 6208 df-map 7329 |
This theorem is referenced by: lincvalpr 31107 ldepspr 31162 |
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