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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 3156 | . 2 |
5 | 1, 4 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1335 wss 3102 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-in 3108 df-ss 3115 |
This theorem is referenced by: undif2ss 3469 pwsnss 3766 iinuniss 3931 brab2a 4639 rncoss 4856 imassrn 4939 rnin 4995 inimass 5002 imadiflem 5249 imainlem 5251 ssoprab2i 5910 npsspw 7391 axresscn 7780 |
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