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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 5437 |
. . 3
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2 | foeq3 5455 |
. . 3
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3 | 1, 2 | anbi12d 473 |
. 2
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4 | df-f1o 5242 |
. 2
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5 | df-f1o 5242 |
. 2
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6 | 3, 4, 5 | 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-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-in 3150 df-ss 3157 df-f 5239 df-f1 5240 df-fo 5241 df-f1o 5242 |
This theorem is referenced by: f1oeq23 5471 f1oeq123d 5474 f1oeq3d 5477 f1ores 5495 resdif 5502 f1osng 5521 f1oresrab 5701 isoeq5 5826 isoini2 5840 mapsnf1o 6762 bren 6772 xpcomf1o 6850 frechashgf1o 10458 sumeq1 11394 fisumss 11431 fsumcnv 11476 prodeq1f 11591 4sqlem11 12432 ennnfonelemhf1o 12463 ennnfonelemex 12464 ssnnctlemct 12496 |
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