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Mirrors > Home > MPE Home > Th. List > setsabs | Structured version Unicode version |
Description: Replacing the same components twice yields the same as the second setting only. (Contributed by Mario Carneiro, 2-Dec-2014.) |
Ref | Expression |
---|---|
setsabs |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | setsres 14319 |
. . . 4
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2 | 1 | adantr 465 |
. . 3
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3 | 2 | uneq1d 3616 |
. 2
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4 | ovex 6224 |
. . . 4
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5 | 4 | a1i 11 |
. . 3
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6 | setsval 14315 |
. . 3
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7 | 5, 6 | sylan 471 |
. 2
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8 | setsval 14315 |
. 2
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9 | 3, 7, 8 | 3eqtr4d 2505 |
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 4520 ax-nul 4528 ax-pr 4638 ax-un 6481 |
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 2649 df-ral 2803 df-rex 2804 df-rab 2807 df-v 3078 df-sbc 3293 df-dif 3438 df-un 3440 df-in 3442 df-ss 3449 df-nul 3745 df-if 3899 df-sn 3985 df-pr 3987 df-op 3991 df-uni 4199 df-br 4400 df-opab 4458 df-id 4743 df-xp 4953 df-rel 4954 df-cnv 4955 df-co 4956 df-dm 4957 df-res 4959 df-iota 5488 df-fun 5527 df-fv 5533 df-ov 6202 df-oprab 6203 df-mpt2 6204 df-sets 14297 |
This theorem is referenced by: ressress 14353 rescabs 14864 |
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