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Mirrors > Home > ILE Home > Th. List > sseqtrd | Unicode version |
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 25-Apr-2004.) |
Ref | Expression |
---|---|
sseqtrd.1 | |
sseqtrd.2 |
Ref | Expression |
---|---|
sseqtrd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseqtrd.1 | . 2 | |
2 | sseqtrd.2 | . . 3 | |
3 | 2 | sseq2d 3097 | . 2 |
4 | 1, 3 | mpbid 146 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 wss 3041 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-in 3047 df-ss 3054 |
This theorem is referenced by: sseqtrrd 3106 fssdmd 5256 resasplitss 5272 nnaword2 6378 erssxp 6420 phpm 6727 ioodisj 9744 tgcl 12160 basgen 12176 bastop1 12179 bastop2 12180 clsss2 12225 topssnei 12258 cnntr 12321 txbasval 12363 neitx 12364 cnmpt1res 12392 cnmpt2res 12393 imasnopn 12395 hmeontr 12409 tgioo 12642 reldvg 12744 dvfvalap 12746 dvbss 12750 dvcnp2cntop 12759 dvaddxxbr 12761 dvmulxxbr 12762 dvcj 12769 nninfalllemn 13129 |
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