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Mirrors > Home > ILE Home > Th. List > smoel2 | Unicode version |
Description: A strictly monotone ordinal function preserves the epsilon relation. (Contributed by Mario Carneiro, 12-Mar-2013.) |
Ref | Expression |
---|---|
smoel2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fndm 5262 |
. . . . . 6
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2 | 1 | eleq2d 2224 |
. . . . 5
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3 | 2 | anbi1d 461 |
. . . 4
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4 | 3 | biimprd 157 |
. . 3
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5 | smoel 6237 |
. . . 4
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6 | 5 | 3expib 1185 |
. . 3
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7 | 4, 6 | sylan9 407 |
. 2
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8 | 7 | imp 123 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1481 ax-10 1482 ax-11 1483 ax-i12 1484 ax-bndl 1486 ax-4 1487 ax-17 1503 ax-i9 1507 ax-ial 1511 ax-i5r 1512 ax-ext 2136 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1740 df-clab 2141 df-cleq 2147 df-clel 2150 df-nfc 2285 df-ral 2437 df-rex 2438 df-v 2711 df-un 3102 df-in 3104 df-ss 3111 df-sn 3562 df-pr 3563 df-op 3565 df-uni 3769 df-br 3962 df-tr 4059 df-iord 4321 df-iota 5128 df-fn 5166 df-fv 5171 df-smo 6223 |
This theorem is referenced by: (None) |
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