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Mirrors > Home > ILE Home > Th. List > issmo | Unicode version |
Description: Conditions for which ![]() |
Ref | Expression |
---|---|
issmo.1 |
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issmo.2 |
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issmo.3 |
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issmo.4 |
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Ref | Expression |
---|---|
issmo |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | issmo.1 |
. . 3
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2 | issmo.4 |
. . . 4
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3 | 2 | feq2i 5274 |
. . 3
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4 | 1, 3 | mpbir 145 |
. 2
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5 | issmo.2 |
. . 3
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6 | ordeq 4302 |
. . . 4
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7 | 2, 6 | ax-mp 5 |
. . 3
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8 | 5, 7 | mpbir 145 |
. 2
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9 | 2 | eleq2i 2207 |
. . . 4
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10 | 2 | eleq2i 2207 |
. . . 4
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11 | issmo.3 |
. . . 4
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12 | 9, 10, 11 | syl2anb 289 |
. . 3
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13 | 12 | rgen2a 2489 |
. 2
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14 | df-smo 6191 |
. 2
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15 | 4, 8, 13, 14 | mpbir3an 1164 |
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 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-in 3082 df-ss 3089 df-uni 3745 df-tr 4035 df-iord 4296 df-fn 5134 df-f 5135 df-smo 6191 |
This theorem is referenced by: iordsmo 6202 |
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