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Mirrors > Home > MPE Home > Th. List > truni | Structured version Visualization version Unicode version |
Description: The union of a class of transitive sets is transitive. Exercise 5(a) of [Enderton] p. 73. (Contributed by Scott Fenton, 21-Feb-2011.) (Proof shortened by Mario Carneiro, 26-Apr-2014.) |
Ref | Expression |
---|---|
truni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | triun 4766 | . 2 | |
2 | uniiun 4573 | . . 3 | |
3 | treq 4758 | . . 3 | |
4 | 2, 3 | ax-mp 5 | . 2 |
5 | 1, 4 | sylibr 224 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wceq 1483 wral 2912 cuni 4436 ciun 4520 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-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-v 3202 df-in 3581 df-ss 3588 df-uni 4437 df-iun 4522 df-tr 4753 |
This theorem is referenced by: dfon2lem1 31688 |
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