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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 3125 | . 2 |
5 | 1, 4 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: 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: undif2ss 3438 pwsnss 3730 iinuniss 3895 brab2a 4592 rncoss 4809 imassrn 4892 rnin 4948 inimass 4955 imadiflem 5202 imainlem 5204 ssoprab2i 5860 npsspw 7279 axresscn 7668 |
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