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Mirrors > Home > ILE Home > Th. List > issmo2 | Unicode version |
Description: Alternate definition of a strictly monotone ordinal function. (Contributed by Mario Carneiro, 12-Mar-2013.) |
Ref | Expression |
---|---|
issmo2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fss 5396 |
. . . . 5
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2 | 1 | ex 115 |
. . . 4
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3 | fdm 5390 |
. . . . 5
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4 | 3 | feq2d 5372 |
. . . 4
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5 | 2, 4 | sylibrd 169 |
. . 3
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6 | ordeq 4390 |
. . . . 5
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7 | 3, 6 | syl 14 |
. . . 4
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8 | 7 | biimprd 158 |
. . 3
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9 | 3 | raleqdv 2692 |
. . . 4
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10 | 9 | biimprd 158 |
. . 3
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11 | 5, 8, 10 | 3anim123d 1330 |
. 2
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12 | dfsmo2 6312 |
. 2
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13 | 11, 12 | imbitrrdi 162 |
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-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-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-in 3150 df-ss 3157 df-uni 3825 df-tr 4117 df-iord 4384 df-fn 5238 df-f 5239 df-smo 6311 |
This theorem is referenced by: (None) |
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