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Mirrors > Home > MPE Home > Th. List > opabbrex | Structured version Visualization version Unicode version |
Description: A collection of ordered pairs with an extension of a binary relation is a set. (Contributed by Alexander van der Vekens, 1-Nov-2017.) (Revised by BJ/AV, 20-Jun-2019.) (Proof shortened by OpenAI, 25-Mar-2020.) |
Ref | Expression |
---|---|
opabbrex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 477 | . 2 | |
2 | pm3.41 582 | . . . . 5 | |
3 | 2 | 2alimi 1740 | . . . 4 |
4 | 3 | adantr 481 | . . 3 |
5 | ssopab2 5001 | . . 3 | |
6 | 4, 5 | syl 17 | . 2 |
7 | 1, 6 | ssexd 4805 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wal 1481 wcel 1990 cvv 3200 wss 3574 class class class wbr 4653 copab 4712 |
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 ax-sep 4781 |
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-v 3202 df-in 3581 df-ss 3588 df-opab 4713 |
This theorem is referenced by: opabresex2d 6696 fvmptopab 6697 sprmpt2d 7350 wlkRes 26546 opabresex0d 41304 |
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