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Mirrors > Home > ILE Home > Th. List > 3brtr3i | Unicode version |
Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 11-Aug-1999.) |
Ref | Expression |
---|---|
3brtr3.1 |
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3brtr3.2 |
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3brtr3.3 |
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Ref | Expression |
---|---|
3brtr3i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3brtr3.2 |
. . 3
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2 | 3brtr3.1 |
. . 3
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3 | 1, 2 | eqbrtrri 4023 |
. 2
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4 | 3brtr3.3 |
. 2
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5 | 3, 4 | breqtri 4025 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-sn 3597 df-pr 3598 df-op 3600 df-br 4001 |
This theorem is referenced by: suplocsrlempr 7784 iap0 9118 ef01bndlem 11735 |
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