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Mirrors > Home > ILE Home > Th. List > eqsstrrd | Unicode version |
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 25-Apr-2004.) |
Ref | Expression |
---|---|
eqsstrrd.1 | |
eqsstrrd.2 |
Ref | Expression |
---|---|
eqsstrrd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqsstrrd.1 | . . 3 | |
2 | 1 | eqcomd 2145 | . 2 |
3 | eqsstrrd.2 | . 2 | |
4 | 2, 3 | eqsstrd 3133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wss 3071 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-in 3077 df-ss 3084 |
This theorem is referenced by: ssxpbm 4974 ssxp1 4975 ssxp2 4976 suppssof1 5999 tfrlemiubacc 6227 tfr1onlemubacc 6243 tfrcllemubacc 6256 oaword1 6367 phplem4dom 6756 fisseneq 6820 archnqq 7225 epttop 12259 metequiv2 12665 limccnpcntop 12813 limccnp2lem 12814 limccnp2cntop 12815 nnsf 13199 |
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