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Mirrors > Home > ILE Home > Th. List > f1eq1 | Unicode version |
Description: Equality theorem for one-to-one functions. (Contributed by NM, 10-Feb-1997.) |
Ref | Expression |
---|---|
f1eq1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | feq1 5360 |
. . 3
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2 | cnveq 4813 |
. . . 4
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3 | 2 | funeqd 5250 |
. . 3
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4 | 1, 3 | anbi12d 473 |
. 2
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5 | df-f1 5233 |
. 2
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6 | df-f1 5233 |
. 2
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7 | 4, 5, 6 | 3bitr4g 223 |
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 |
This theorem is referenced by: f1oeq1 5461 f1eq123d 5465 fun11iun 5494 fo00 5509 tposf12 6284 f1dom2g 6770 f1domg 6772 dom3d 6788 domtr 6799 djudom 7106 difinfsn 7113 djudoml 7232 djudomr 7233 nninfdc 12468 conjsubgen 13172 |
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