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Mirrors > Home > MPE Home > Th. List > Mathboxes > br2ndeq | Structured version Unicode version |
Description: Uniqueness condition for
binary relationship over the ![]() |
Ref | Expression |
---|---|
br2ndeq.1 |
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br2ndeq.2 |
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br2ndeq.3 |
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Ref | Expression |
---|---|
br2ndeq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | br2ndeq.1 |
. . . 4
![]() ![]() ![]() ![]() | |
2 | br2ndeq.2 |
. . . 4
![]() ![]() ![]() ![]() | |
3 | 1, 2 | op2nd 6686 |
. . 3
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4 | 3 | eqeq1i 2458 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | fo2nd 6697 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() | |
6 | fofn 5720 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 5, 6 | ax-mp 5 |
. . 3
![]() ![]() ![]() ![]() |
8 | opex 4654 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | fnbrfvb 5831 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 7, 8, 9 | mp2an 672 |
. 2
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11 | eqcom 2460 |
. 2
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12 | 4, 10, 11 | 3bitr3i 275 |
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 1952 ax-ext 2430 ax-sep 4511 ax-nul 4519 ax-pow 4568 ax-pr 4629 ax-un 6472 |
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 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-ral 2800 df-rex 2801 df-rab 2804 df-v 3070 df-sbc 3285 df-dif 3429 df-un 3431 df-in 3433 df-ss 3440 df-nul 3736 df-if 3890 df-sn 3976 df-pr 3978 df-op 3982 df-uni 4190 df-br 4391 df-opab 4449 df-mpt 4450 df-id 4734 df-xp 4944 df-rel 4945 df-cnv 4946 df-co 4947 df-dm 4948 df-rn 4949 df-iota 5479 df-fun 5518 df-fn 5519 df-f 5520 df-fo 5522 df-fv 5524 df-2nd 6678 |
This theorem is referenced by: dfrn5 27722 brtxp 28045 brpprod 28050 elfuns 28080 brimg 28102 brcup 28104 brcap 28105 brrestrict 28114 |
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