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Mirrors > Home > MPE Home > Th. List > ssoprab2 | Structured version Visualization version Unicode version |
Description: Equivalence of ordered pair abstraction subclass and implication. Compare ssopab2 5001. (Contributed by FL, 6-Nov-2013.) (Proof shortened by Mario Carneiro, 11-Dec-2016.) |
Ref | Expression |
---|---|
ssoprab2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . . . . . . 7 | |
2 | 1 | anim2d 589 | . . . . . 6 |
3 | 2 | aleximi 1759 | . . . . 5 |
4 | 3 | aleximi 1759 | . . . 4 |
5 | 4 | aleximi 1759 | . . 3 |
6 | 5 | ss2abdv 3675 | . 2 |
7 | df-oprab 6654 | . 2 | |
8 | df-oprab 6654 | . 2 | |
9 | 6, 7, 8 | 3sstr4g 3646 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wal 1481 wceq 1483 wex 1704 cab 2608 wss 3574 cop 4183 coprab 6651 |
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-in 3581 df-ss 3588 df-oprab 6654 |
This theorem is referenced by: ssoprab2b 6712 joinfval 17001 meetfval 17015 |
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