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Mirrors > Home > MPE Home > Th. List > mptun | Structured version Visualization version Unicode version |
Description: Union of mappings which are mutually compatible. (Contributed by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
mptun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mpt 4730 | . 2 | |
2 | df-mpt 4730 | . . . 4 | |
3 | df-mpt 4730 | . . . 4 | |
4 | 2, 3 | uneq12i 3765 | . . 3 |
5 | elun 3753 | . . . . . . 7 | |
6 | 5 | anbi1i 731 | . . . . . 6 |
7 | andir 912 | . . . . . 6 | |
8 | 6, 7 | bitri 264 | . . . . 5 |
9 | 8 | opabbii 4717 | . . . 4 |
10 | unopab 4728 | . . . 4 | |
11 | 9, 10 | eqtr4i 2647 | . . 3 |
12 | 4, 11 | eqtr4i 2647 | . 2 |
13 | 1, 12 | eqtr4i 2647 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wo 383 wa 384 wceq 1483 wcel 1990 cun 3572 copab 4712 cmpt 4729 |
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-v 3202 df-un 3579 df-opab 4713 df-mpt 4730 |
This theorem is referenced by: fmptap 6436 fmptapd 6437 partfun 29475 esumrnmpt2 30130 ptrest 33408 |
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