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Mirrors > Home > ILE Home > Th. List > 3sstr3i | Unicode version |
Description: Substitution of equality in both sides of a subclass relationship. (Contributed by NM, 13-Jan-1996.) (Proof shortened by Eric Schmidt, 26-Jan-2007.) |
Ref | Expression |
---|---|
3sstr3.1 | |
3sstr3.2 | |
3sstr3.3 |
Ref | Expression |
---|---|
3sstr3i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3sstr3.1 | . 2 | |
2 | 3sstr3.2 | . . 3 | |
3 | 3sstr3.3 | . . 3 | |
4 | 2, 3 | sseq12i 3165 | . 2 |
5 | 1, 4 | mpbi 144 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 wss 3111 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-in 3117 df-ss 3124 |
This theorem is referenced by: (None) |
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