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Mirrors > Home > MPE Home > Th. List > kmlem10 | Structured version Visualization version Unicode version |
Description: Lemma for 5-quantifier AC of Kurt Maes, Th. 4, part of 3 => 4. (Contributed by NM, 25-Mar-2004.) |
Ref | Expression |
---|---|
kmlem9.1 |
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Ref | Expression |
---|---|
kmlem10 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | kmlem9.1 |
. . 3
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2 | 1 | kmlem9 8619 |
. 2
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3 | vex 3060 |
. . . . 5
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4 | 3 | abrexex 6799 |
. . . 4
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5 | 1, 4 | eqeltri 2536 |
. . 3
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6 | raleq 2999 |
. . . . 5
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7 | 6 | raleqbi1dv 3007 |
. . . 4
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8 | raleq 2999 |
. . . . 5
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9 | 8 | exbidv 1779 |
. . . 4
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10 | 7, 9 | imbi12d 326 |
. . 3
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11 | 5, 10 | spcv 3152 |
. 2
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12 | 2, 11 | mpi 20 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-8 1900 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-rep 4531 ax-sep 4541 ax-nul 4550 ax-pr 4656 ax-un 6615 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rex 2755 df-reu 2756 df-rab 2758 df-v 3059 df-sbc 3280 df-csb 3376 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-sn 3981 df-pr 3983 df-op 3987 df-uni 4213 df-iun 4294 df-br 4419 df-opab 4478 df-mpt 4479 df-id 4771 df-xp 4862 df-rel 4863 df-cnv 4864 df-co 4865 df-dm 4866 df-rn 4867 df-res 4868 df-ima 4869 df-iota 5569 df-fun 5607 df-fn 5608 df-f 5609 df-f1 5610 df-fo 5611 df-f1o 5612 df-fv 5613 |
This theorem is referenced by: kmlem13 8623 |
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