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Mirrors > Home > ILE Home > Th. List > eqrel | Unicode version |
Description: Extensionality principle for relations. Theorem 3.2(ii) of [Monk1] p. 33. (Contributed by NM, 2-Aug-1994.) |
Ref | Expression |
---|---|
eqrel |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssrel 4526 |
. . 3
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2 | ssrel 4526 |
. . 3
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3 | 1, 2 | bi2anan9 573 |
. 2
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4 | eqss 3040 |
. 2
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5 | 2albiim 1422 |
. 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-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 ax-pow 4009 ax-pr 4036 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-v 2621 df-un 3003 df-in 3005 df-ss 3012 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-opab 3900 df-xp 4444 df-rel 4445 |
This theorem is referenced by: eqrelriv 4531 eqrelrdv 4534 eqbrrdv 4535 eqrelrdv2 4537 opabid2 4567 reldm0 4654 iss 4758 asymref 4817 funssres 5056 fsn 5469 |
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