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Mirrors > Home > ILE Home > Th. List > sseqtri | Unicode version |
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 28-Jul-1995.) |
Ref | Expression |
---|---|
sseqtr.1 | |
sseqtr.2 |
Ref | Expression |
---|---|
sseqtri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseqtr.1 | . 2 | |
2 | sseqtr.2 | . . 3 | |
3 | 2 | sseq2i 3024 | . 2 |
4 | 1, 3 | mpbi 143 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1284 wss 2973 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-in 2979 df-ss 2986 |
This theorem is referenced by: sseqtr4i 3032 eqimssi 3053 abssi 3069 ssun2 3136 inssddif 3205 difdifdirss 3327 pwundifss 4040 unixpss 4469 0ima 4705 |
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