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Mirrors > Home > ILE Home > Th. List > f1oeq2 | Unicode version |
Description: Equality theorem for one-to-one onto functions. (Contributed by NM, 10-Feb-1997.) |
Ref | Expression |
---|---|
f1oeq2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1eq2 5332 |
. . 3
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2 | foeq2 5350 |
. . 3
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3 | 1, 2 | anbi12d 465 |
. 2
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4 | df-f1o 5138 |
. 2
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5 | df-f1o 5138 |
. 2
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6 | 3, 4, 5 | 3bitr4g 222 |
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-5 1424 ax-gen 1426 ax-4 1488 ax-17 1507 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-cleq 2133 df-fn 5134 df-f 5135 df-f1 5136 df-fo 5137 df-f1o 5138 |
This theorem is referenced by: f1oeq23 5367 f1oeq123d 5370 f1oeq2d 5371 f1osng 5416 isoeq4 5713 bren 6649 f1dmvrnfibi 6840 summodclem3 11181 summodclem2a 11182 summodc 11184 fsum3 11188 fsumf1o 11191 sumsnf 11210 |
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