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Mathbox for Giovanni Mascellani |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ac6s6f | Structured version Visualization version Unicode version |
Description: Generalization of the Axiom of Choice to classes, moving the existence condition in the consequent. (Contributed by Giovanni Mascellani, 20-Aug-2018.) |
Ref | Expression |
---|---|
ac6s6f.1 |
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ac6s6f.2 |
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ac6s6f.3 |
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ac6s6f.4 |
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Ref | Expression |
---|---|
ac6s6f |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ac6s6f.1 |
. . . . . 6
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2 | 1 | isseti 3063 |
. . . . 5
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3 | ac6s6f.2 |
. . . . . 6
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4 | vex 3060 |
. . . . . 6
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5 | ac6s6f.3 |
. . . . . 6
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6 | 3, 4, 5 | ac6s6 32461 |
. . . . 5
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7 | 2, 6 | pm3.2i 461 |
. . . 4
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8 | 7 | exan 2064 |
. . 3
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9 | exdistr 1846 |
. . 3
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10 | 8, 9 | mpbir 214 |
. 2
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11 | nfcv 2603 |
. . . . 5
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12 | ac6s6f.4 |
. . . . 5
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13 | 11, 12 | raleqf 2995 |
. . . 4
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14 | 13 | biimpa 491 |
. . 3
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15 | 14 | 2eximi 1719 |
. 2
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16 | ax5e 1771 |
. 2
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17 | 10, 15, 16 | mp2b 10 |
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-pow 4598 ax-pr 4656 ax-un 6615 ax-reg 8138 ax-inf2 8177 ax-ac2 8924 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3or 992 df-3an 993 df-tru 1458 df-fal 1461 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-rmo 2757 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-pss 3432 df-nul 3744 df-if 3894 df-pw 3965 df-sn 3981 df-pr 3983 df-tp 3985 df-op 3987 df-uni 4213 df-int 4249 df-iun 4294 df-iin 4295 df-br 4419 df-opab 4478 df-mpt 4479 df-tr 4514 df-eprel 4767 df-id 4771 df-po 4777 df-so 4778 df-fr 4815 df-se 4816 df-we 4817 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-pred 5403 df-ord 5449 df-on 5450 df-lim 5451 df-suc 5452 df-iota 5569 df-fun 5607 df-fn 5608 df-f 5609 df-f1 5610 df-fo 5611 df-f1o 5612 df-fv 5613 df-isom 5614 df-riota 6282 df-om 6725 df-wrecs 7059 df-recs 7121 df-rdg 7159 df-en 7601 df-r1 8266 df-rank 8267 df-card 8404 df-ac 8578 |
This theorem is referenced by: (None) |
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