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Mirrors > Home > ILE Home > Th. List > trel3 | Unicode version |
Description: In a transitive class, the membership relation is transitive. (Contributed by NM, 19-Apr-1994.) |
Ref | Expression |
---|---|
trel3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anass 971 | . . 3 | |
2 | trel 4082 | . . . 4 | |
3 | 2 | anim2d 335 | . . 3 |
4 | 1, 3 | syl5bi 151 | . 2 |
5 | trel 4082 | . 2 | |
6 | 4, 5 | syld 45 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 967 wcel 2135 wtr 4075 |
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-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 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-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2724 df-in 3118 df-ss 3125 df-uni 3785 df-tr 4076 |
This theorem is referenced by: (None) |
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