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Mirrors > Home > MPE Home > Th. List > Mathboxes > untint | Structured version Visualization version Unicode version |
Description: If there is an untangled element of a class, then the intersection of the class is untangled. (Contributed by Scott Fenton, 1-Mar-2011.) |
Ref | Expression |
---|---|
untint |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | intss1 4492 | . . 3 | |
2 | ssralv 3666 | . . 3 | |
3 | 1, 2 | syl 17 | . 2 |
4 | 3 | rexlimiv 3027 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wcel 1990 wral 2912 wrex 2913 wss 3574 cint 4475 |
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-int 4476 |
This theorem is referenced by: (None) |
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