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Mirrors > Home > MPE Home > Th. List > trel3 | Structured version Visualization version 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 1042 | . . 3 | |
2 | trel 4759 | . . . 4 | |
3 | 2 | anim2d 589 | . . 3 |
4 | 1, 3 | syl5bi 232 | . 2 |
5 | trel 4759 | . 2 | |
6 | 4, 5 | syld 47 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wcel 1990 wtr 4752 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-in 3581 df-ss 3588 df-uni 4437 df-tr 4753 |
This theorem is referenced by: ordelord 5745 |
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