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Mirrors > Home > ILE Home > Th. List > snnen2og | Unicode version |
Description: A singleton ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
snnen2og |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1onn 6539 |
. . 3
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2 | php5 6876 |
. . 3
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3 | 1, 2 | ax-mp 5 |
. 2
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4 | ensn1g 6815 |
. 2
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5 | df-2o 6436 |
. . . . 5
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6 | 5 | eqcomi 2193 |
. . . 4
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7 | 6 | breq2i 4026 |
. . 3
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8 | ensymb 6798 |
. . . . 5
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9 | entr 6802 |
. . . . . 6
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10 | 9 | ex 115 |
. . . . 5
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11 | 8, 10 | sylbi 121 |
. . . 4
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12 | 11 | con3rr3 634 |
. . 3
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13 | 7, 12 | sylnbi 679 |
. 2
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14 | 3, 4, 13 | mpsyl 65 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-nul 4144 ax-pow 4189 ax-pr 4224 ax-un 4448 ax-setind 4551 ax-iinf 4602 |
This theorem depends on definitions: df-bi 117 df-dc 836 df-3or 981 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-sbc 2978 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-nul 3438 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-int 3860 df-br 4019 df-opab 4080 df-tr 4117 df-id 4308 df-iord 4381 df-on 4383 df-suc 4386 df-iom 4605 df-xp 4647 df-rel 4648 df-cnv 4649 df-co 4650 df-dm 4651 df-rn 4652 df-res 4653 df-ima 4654 df-iota 5193 df-fun 5233 df-fn 5234 df-f 5235 df-f1 5236 df-fo 5237 df-f1o 5238 df-fv 5239 df-1o 6435 df-2o 6436 df-er 6553 df-en 6759 |
This theorem is referenced by: (None) |
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