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Mirrors > Home > MPE Home > Th. List > axdc3lem3 | Structured version Unicode version |
Description: Simple substitution lemma for axdc3 8721. (Contributed by Mario Carneiro, 27-Jan-2013.) |
Ref | Expression |
---|---|
axdc3lem3.1 |
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axdc3lem3.2 |
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axdc3lem3.3 |
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Ref | Expression |
---|---|
axdc3lem3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axdc3lem3.2 |
. . 3
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2 | 1 | eleq2i 2527 |
. 2
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3 | axdc3lem3.3 |
. . 3
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4 | feq1 5637 |
. . . . 5
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5 | fveq1 5785 |
. . . . . 6
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6 | 5 | eqeq1d 2453 |
. . . . 5
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7 | fveq1 5785 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | fveq1 5785 |
. . . . . . . 8
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9 | 8 | fveq2d 5790 |
. . . . . . 7
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10 | 7, 9 | eleq12d 2531 |
. . . . . 6
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11 | 10 | ralbidv 2839 |
. . . . 5
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12 | 4, 6, 11 | 3anbi123d 1290 |
. . . 4
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13 | 12 | rexbidv 2840 |
. . 3
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14 | 3, 13 | elab 3200 |
. 2
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15 | suceq 4879 |
. . . . 5
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16 | 15 | feq2d 5642 |
. . . 4
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17 | raleq 3010 |
. . . 4
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18 | 16, 17 | 3anbi13d 1292 |
. . 3
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19 | 18 | cbvrexv 3041 |
. 2
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20 | 2, 14, 19 | 3bitri 271 |
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-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 |
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-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2599 df-ral 2798 df-rex 2799 df-rab 2802 df-v 3067 df-dif 3426 df-un 3428 df-in 3430 df-ss 3437 df-nul 3733 df-if 3887 df-sn 3973 df-pr 3975 df-op 3979 df-uni 4187 df-br 4388 df-opab 4446 df-suc 4820 df-rel 4942 df-cnv 4943 df-co 4944 df-dm 4945 df-rn 4946 df-iota 5476 df-fun 5515 df-fn 5516 df-f 5517 df-fv 5521 |
This theorem is referenced by: axdc3lem4 8720 |
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