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Mirrors > Home > ILE Home > Th. List > rneqd | Unicode version |
Description: Equality deduction for range. (Contributed by NM, 4-Mar-2004.) |
Ref | Expression |
---|---|
rneqd.1 |
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Ref | Expression |
---|---|
rneqd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rneqd.1 |
. 2
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2 | rneq 4850 |
. 2
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3 | 1, 2 | syl 14 |
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-in 3135 df-ss 3142 df-sn 3597 df-pr 3598 df-op 3600 df-br 4001 df-opab 4062 df-cnv 4631 df-dm 4633 df-rn 4634 |
This theorem is referenced by: resima2 4937 imaeq1 4961 imaeq2 4962 resiima 4982 elxp4 5112 elxp5 5113 funimacnv 5288 funimaexg 5296 fnima 5330 fnrnfv 5558 2ndvalg 6138 fo2nd 6153 f2ndres 6155 en1 6793 xpassen 6824 xpdom2 6825 sbthlemi4 6953 djudom 7086 exmidfodomrlemim 7194 seqeq1 10431 seqeq2 10432 seqeq3 10433 seq3val 10441 seqvalcd 10442 ennnfonelemex 12395 ennnfonelemf1 12399 restval 12639 restid2 12642 tgrest 13329 txvalex 13414 txval 13415 mopnval 13602 |
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