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Mirrors > Home > ILE Home > Th. List > f1oeq1 | Unicode version |
Description: Equality theorem for one-to-one onto functions. (Contributed by NM, 10-Feb-1997.) |
Ref | Expression |
---|---|
f1oeq1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1eq1 5087 |
. . 3
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2 | foeq1 5102 |
. . 3
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3 | 1, 2 | anbi12d 442 |
. 2
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4 | df-f1o 4909 |
. 2
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5 | df-f1o 4909 |
. 2
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6 | 3, 4, 5 | 3bitr4g 212 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-fun 4904 df-fn 4905 df-f 4906 df-f1 4907 df-fo 4908 df-f1o 4909 |
This theorem is referenced by: f1oeq123d 5123 f1ocnvb 5140 f1orescnv 5142 f1ovi 5165 f1osng 5167 f1oresrab 5329 fsn 5335 isoeq1 5441 f1oen3g 6234 ensn1 6276 xpcomf1o 6299 |
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