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Mirrors > Home > ILE Home > Th. List > f1oeq3 | Unicode version |
Description: Equality theorem for one-to-one onto functions. (Contributed by NM, 10-Feb-1997.) |
Ref | Expression |
---|---|
f1oeq3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1eq3 5213 |
. . 3
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2 | foeq3 5231 |
. . 3
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3 | 1, 2 | anbi12d 457 |
. 2
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4 | df-f1o 5022 |
. 2
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5 | df-f1o 5022 |
. 2
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6 | 3, 4, 5 | 3bitr4g 221 |
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 104 ax-ia2 105 ax-ia3 106 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-11 1442 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-in 3005 df-ss 3012 df-f 5019 df-f1 5020 df-fo 5021 df-f1o 5022 |
This theorem is referenced by: f1oeq23 5247 f1oeq123d 5250 f1ores 5268 resdif 5275 f1osng 5294 f1oresrab 5463 isoeq5 5584 isoini2 5598 bren 6464 xpcomf1o 6541 frechashgf1o 9835 sumeq1 10744 fisumss 10784 fsumcnv 10831 |
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