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Mirrors > Home > MPE Home > Th. List > iinss1 | Structured version Visualization version Unicode version |
Description: Subclass theorem for indexed intersection. (Contributed by NM, 24-Jan-2012.) |
Ref | Expression |
---|---|
iinss1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssralv 3666 | . . 3 | |
2 | vex 3203 | . . . 4 | |
3 | eliin 4525 | . . . 4 | |
4 | 2, 3 | ax-mp 5 | . . 3 |
5 | eliin 4525 | . . . 4 | |
6 | 2, 5 | ax-mp 5 | . . 3 |
7 | 1, 4, 6 | 3imtr4g 285 | . 2 |
8 | 7 | ssrdv 3609 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wcel 1990 wral 2912 cvv 3200 wss 3574 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-in 3581 df-ss 3588 df-iin 4523 |
This theorem is referenced by: polcon3N 35203 smflimsuplem5 41030 smflimsuplem7 41032 |
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