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Mirrors > Home > MPE Home > Th. List > opi1 | Structured version Visualization version Unicode version |
Description: One of the two elements in an ordered pair. (Contributed by NM, 15-Jul-1993.) (Revised by Mario Carneiro, 26-Apr-2015.) (Avoid depending on this detail.) |
Ref | Expression |
---|---|
opi1.1 | |
opi1.2 |
Ref | Expression |
---|---|
opi1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snex 4908 | . . 3 | |
2 | 1 | prid1 4297 | . 2 |
3 | opi1.1 | . . 3 | |
4 | opi1.2 | . . 3 | |
5 | 3, 4 | dfop 4401 | . 2 |
6 | 2, 5 | eleqtrri 2700 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wcel 1990 cvv 3200 csn 4177 cpr 4179 cop 4183 |
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-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 |
This theorem is referenced by: opth1 4944 opth 4945 |
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