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Mirrors > Home > ILE Home > Th. List > 3sstr4i | 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 |
---|---|
3sstr4.1 | |
3sstr4.2 | |
3sstr4.3 |
Ref | Expression |
---|---|
3sstr4i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3sstr4.1 | . 2 | |
2 | 3sstr4.2 | . . 3 | |
3 | 3sstr4.3 | . . 3 | |
4 | 2, 3 | sseq12i 3175 | . 2 |
5 | 1, 4 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1348 wss 3121 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-in 3127 df-ss 3134 |
This theorem is referenced by: undif2ss 3490 pwsnss 3790 iinuniss 3955 brab2a 4664 rncoss 4881 imassrn 4964 rnin 5020 inimass 5027 imadiflem 5277 imainlem 5279 ssoprab2i 5942 npsspw 7433 axresscn 7822 |
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