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Mirrors > Home > MPE Home > Th. List > iunxprg | Structured version Visualization version Unicode version |
Description: A pair index picks out two instances of an indexed union's argument. (Contributed by Alexander van der Vekens, 2-Feb-2018.) |
Ref | Expression |
---|---|
iunxprg.1 | |
iunxprg.2 |
Ref | Expression |
---|---|
iunxprg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pr 4180 | . . . 4 | |
2 | iuneq1 4534 | . . . 4 | |
3 | 1, 2 | ax-mp 5 | . . 3 |
4 | iunxun 4605 | . . 3 | |
5 | 3, 4 | eqtri 2644 | . 2 |
6 | iunxprg.1 | . . . . 5 | |
7 | 6 | iunxsng 4602 | . . . 4 |
8 | 7 | adantr 481 | . . 3 |
9 | iunxprg.2 | . . . . 5 | |
10 | 9 | iunxsng 4602 | . . . 4 |
11 | 10 | adantl 482 | . . 3 |
12 | 8, 11 | uneq12d 3768 | . 2 |
13 | 5, 12 | syl5eq 2668 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cun 3572 csn 4177 cpr 4179 ciun 4520 |
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-ral 2917 df-rex 2918 df-v 3202 df-sbc 3436 df-un 3579 df-in 3581 df-ss 3588 df-sn 4178 df-pr 4180 df-iun 4522 |
This theorem is referenced by: ovnsubadd2lem 40859 rnfdmpr 41300 |
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