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Mirrors > Home > ILE Home > Th. List > f1oeq123d | Unicode version |
Description: Equality deduction for one-to-one onto functions. (Contributed by Mario Carneiro, 27-Jan-2017.) |
Ref | Expression |
---|---|
f1eq123d.1 |
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f1eq123d.2 |
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f1eq123d.3 |
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Ref | Expression |
---|---|
f1oeq123d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1eq123d.1 |
. . 3
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2 | f1oeq1 5364 |
. . 3
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3 | 1, 2 | syl 14 |
. 2
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4 | f1eq123d.2 |
. . 3
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5 | f1oeq2 5365 |
. . 3
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6 | 4, 5 | syl 14 |
. 2
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7 | f1eq123d.3 |
. . 3
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8 | f1oeq3 5366 |
. . 3
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9 | 7, 8 | syl 14 |
. 2
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10 | 3, 6, 9 | 3bitrd 213 |
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-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 df-opab 3998 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-fun 5133 df-fn 5134 df-f 5135 df-f1 5136 df-fo 5137 df-f1o 5138 |
This theorem is referenced by: f1oprg 5419 ennnfonelemhf1o 11962 |
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