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Mirrors > Home > MPE Home > Th. List > dfrab3ss | Structured version Visualization version Unicode version |
Description: Restricted class abstraction with a common superset. (Contributed by Stefan O'Rear, 12-Sep-2015.) (Proof shortened by Mario Carneiro, 8-Nov-2015.) |
Ref | Expression |
---|---|
dfrab3ss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ss 3588 | . . 3 | |
2 | ineq1 3807 | . . . 4 | |
3 | 2 | eqcomd 2628 | . . 3 |
4 | 1, 3 | sylbi 207 | . 2 |
5 | dfrab3 3902 | . 2 | |
6 | dfrab3 3902 | . . . 4 | |
7 | 6 | ineq2i 3811 | . . 3 |
8 | inass 3823 | . . 3 | |
9 | 7, 8 | eqtr4i 2647 | . 2 |
10 | 4, 5, 9 | 3eqtr4g 2681 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 cab 2608 crab 2916 cin 3573 wss 3574 |
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-rab 2921 df-v 3202 df-in 3581 df-ss 3588 |
This theorem is referenced by: mbfposadd 33457 proot1hash 37778 |
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