Mathbox for Thierry Arnoux |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > uniinn0 | Structured version Visualization version Unicode version |
Description: Sufficient and necessary condition for a union to intersect with a given set. (Contributed by Thierry Arnoux, 27-Jan-2020.) |
Ref | Expression |
---|---|
uniinn0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nne 2798 | . . . 4 | |
2 | 1 | ralbii 2980 | . . 3 |
3 | ralnex 2992 | . . 3 | |
4 | unissb 4469 | . . . 4 | |
5 | disj2 4024 | . . . 4 | |
6 | disj2 4024 | . . . . 5 | |
7 | 6 | ralbii 2980 | . . . 4 |
8 | 4, 5, 7 | 3bitr4ri 293 | . . 3 |
9 | 2, 3, 8 | 3bitr3i 290 | . 2 |
10 | 9 | necon1abii 2842 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 196 wceq 1483 wne 2794 wral 2912 wrex 2913 cvv 3200 cdif 3571 cin 3573 wss 3574 c0 3915 cuni 4436 |
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-ne 2795 df-ral 2917 df-rex 2918 df-v 3202 df-dif 3577 df-in 3581 df-ss 3588 df-nul 3916 df-uni 4437 |
This theorem is referenced by: locfinreflem 29907 |
Copyright terms: Public domain | W3C validator |