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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 5461 |
. . 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 5462 |
. . 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 5463 |
. . 3
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9 | 7, 8 | syl 14 |
. 2
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10 | 3, 6, 9 | 3bitrd 214 |
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 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-v 2751 df-un 3145 df-in 3147 df-ss 3154 df-sn 3610 df-pr 3611 df-op 3613 df-br 4016 df-opab 4077 df-rel 4645 df-cnv 4646 df-co 4647 df-dm 4648 df-rn 4649 df-fun 5230 df-fn 5231 df-f 5232 df-f1 5233 df-fo 5234 df-f1o 5235 |
This theorem is referenced by: f1oprg 5517 ennnfonelemhf1o 12428 |
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