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Mirrors > Home > MPE Home > Th. List > caovass | Structured version Unicode version |
Description: Convert an operation associative law to class notation. (Contributed by NM, 26-Aug-1995.) (Revised by Mario Carneiro, 26-May-2014.) |
Ref | Expression |
---|---|
caovass.1 |
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caovass.2 |
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caovass.3 |
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caovass.4 |
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Ref | Expression |
---|---|
caovass |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovass.1 |
. 2
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2 | caovass.2 |
. 2
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3 | caovass.3 |
. 2
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4 | tru 1374 |
. . 3
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5 | caovass.4 |
. . . . 5
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6 | 5 | a1i 11 |
. . . 4
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7 | 6 | caovassg 6358 |
. . 3
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8 | 4, 7 | mpan 670 |
. 2
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9 | 1, 2, 3, 8 | mp3an 1315 |
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-iota 5476 df-fv 5521 df-ov 6190 |
This theorem is referenced by: caov32 6387 caov12 6388 caov31 6389 caov13 6390 caov4 6391 caov411 6392 caovdilem 6395 caovmo 6397 |
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