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Mirrors > Home > MPE Home > Th. List > omina | Structured version Unicode version |
Description: ![]() ![]() ![]() |
Ref | Expression |
---|---|
omina |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | peano1 6595 |
. . 3
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2 | ne0i 3741 |
. . 3
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3 | 1, 2 | ax-mp 5 |
. 2
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4 | cfom 8534 |
. 2
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5 | nnfi 7604 |
. . . . 5
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6 | pwfi 7707 |
. . . . 5
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7 | 5, 6 | sylib 196 |
. . . 4
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8 | isfinite 7959 |
. . . 4
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9 | 7, 8 | sylib 196 |
. . 3
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10 | 9 | rgen 2889 |
. 2
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11 | elina 8955 |
. 2
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12 | 3, 4, 10, 11 | mpbir3an 1170 |
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 1952 ax-ext 2430 ax-rep 4501 ax-sep 4511 ax-nul 4519 ax-pow 4568 ax-pr 4629 ax-un 6472 ax-inf2 7948 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 966 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-ral 2800 df-rex 2801 df-reu 2802 df-rmo 2803 df-rab 2804 df-v 3070 df-sbc 3285 df-csb 3387 df-dif 3429 df-un 3431 df-in 3433 df-ss 3440 df-pss 3442 df-nul 3736 df-if 3890 df-pw 3960 df-sn 3976 df-pr 3978 df-tp 3980 df-op 3982 df-uni 4190 df-int 4227 df-iun 4271 df-iin 4272 df-br 4391 df-opab 4449 df-mpt 4450 df-tr 4484 df-eprel 4730 df-id 4734 df-po 4739 df-so 4740 df-fr 4777 df-se 4778 df-we 4779 df-ord 4820 df-on 4821 df-lim 4822 df-suc 4823 df-xp 4944 df-rel 4945 df-cnv 4946 df-co 4947 df-dm 4948 df-rn 4949 df-res 4950 df-ima 4951 df-iota 5479 df-fun 5518 df-fn 5519 df-f 5520 df-f1 5521 df-fo 5522 df-f1o 5523 df-fv 5524 df-isom 5525 df-riota 6151 df-ov 6193 df-oprab 6194 df-mpt2 6195 df-om 6577 df-1st 6677 df-2nd 6678 df-recs 6932 df-rdg 6966 df-1o 7020 df-2o 7021 df-oadd 7024 df-er 7201 df-map 7316 df-en 7411 df-dom 7412 df-sdom 7413 df-fin 7414 df-card 8210 df-cf 8212 df-ina 8953 |
This theorem is referenced by: r1omALT 9044 r1omtsk 9047 |
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