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Mirrors > Home > MPE Home > Th. List > iinun2 | Structured version Visualization version Unicode version |
Description: Indexed intersection of union. Generalization of half of theorem "Distributive laws" in [Enderton] p. 30. Use intiin 4574 to recover Enderton's theorem. (Contributed by NM, 19-Aug-2004.) |
Ref | Expression |
---|---|
iinun2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.32v 3083 | . . . 4 | |
2 | elun 3753 | . . . . 5 | |
3 | 2 | ralbii 2980 | . . . 4 |
4 | vex 3203 | . . . . . 6 | |
5 | eliin 4525 | . . . . . 6 | |
6 | 4, 5 | ax-mp 5 | . . . . 5 |
7 | 6 | orbi2i 541 | . . . 4 |
8 | 1, 3, 7 | 3bitr4i 292 | . . 3 |
9 | eliin 4525 | . . . 4 | |
10 | 4, 9 | ax-mp 5 | . . 3 |
11 | elun 3753 | . . 3 | |
12 | 8, 10, 11 | 3bitr4i 292 | . 2 |
13 | 12 | eqriv 2619 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wo 383 wceq 1483 wcel 1990 wral 2912 cvv 3200 cun 3572 ciin 4521 |
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-v 3202 df-un 3579 df-iin 4523 |
This theorem is referenced by: (None) |
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