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Mirrors > Home > MPE Home > Th. List > resopab | Structured version Visualization version Unicode version |
Description: Restriction of a class abstraction of ordered pairs. (Contributed by NM, 5-Nov-2002.) |
Ref | Expression |
---|---|
resopab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-res 5126 | . 2 | |
2 | df-xp 5120 | . . . . . 6 | |
3 | vex 3203 | . . . . . . . 8 | |
4 | 3 | biantru 526 | . . . . . . 7 |
5 | 4 | opabbii 4717 | . . . . . 6 |
6 | 2, 5 | eqtr4i 2647 | . . . . 5 |
7 | 6 | ineq2i 3811 | . . . 4 |
8 | incom 3805 | . . . 4 | |
9 | 7, 8 | eqtri 2644 | . . 3 |
10 | inopab 5252 | . . 3 | |
11 | 9, 10 | eqtri 2644 | . 2 |
12 | 1, 11 | eqtri 2644 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 384 wceq 1483 wcel 1990 cvv 3200 cin 3573 copab 4712 cxp 5112 cres 5116 |
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 df-xp 5120 df-rel 5121 df-res 5126 |
This theorem is referenced by: resopab2 5448 opabresid 5455 mptpreima 5628 isarep2 5978 resoprab 6756 elrnmpt2res 6774 df1st2 7263 df2nd2 7264 |
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