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Mirrors > Home > MPE Home > Th. List > Mathboxes > opelopab4 | Structured version Visualization version Unicode version |
Description: Ordered pair membership in a class abstraction of pairs. Compare to elopab 4983. (Contributed by Alan Sare, 8-Feb-2014.) (Revised by Mario Carneiro, 6-May-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
opelopab4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elopab 4983 | . 2 | |
2 | vex 3203 | . . . . . 6 | |
3 | vex 3203 | . . . . . 6 | |
4 | 2, 3 | opth 4945 | . . . . 5 |
5 | eqcom 2629 | . . . . 5 | |
6 | 4, 5 | bitr3i 266 | . . . 4 |
7 | 6 | anbi1i 731 | . . 3 |
8 | 7 | 2exbii 1775 | . 2 |
9 | 1, 8 | bitr4i 267 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wceq 1483 wex 1704 wcel 1990 cop 4183 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 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 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-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-opab 4713 |
This theorem is referenced by: (None) |
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