Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > brab2a | Unicode version |
Description: Ordered pair membership in an ordered pair class abstraction. (Contributed by Mario Carneiro, 9-Nov-2015.) |
Ref | Expression |
---|---|
brab2a.1 | |
brab2a.2 |
Ref | Expression |
---|---|
brab2a |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 108 | . . . . 5 | |
2 | 1 | ssopab2i 4250 | . . . 4 |
3 | brab2a.2 | . . . 4 | |
4 | df-xp 4605 | . . . 4 | |
5 | 2, 3, 4 | 3sstr4i 3179 | . . 3 |
6 | 5 | brel 4651 | . 2 |
7 | df-br 3978 | . . . 4 | |
8 | 3 | eleq2i 2231 | . . . 4 |
9 | 7, 8 | bitri 183 | . . 3 |
10 | brab2a.1 | . . . 4 | |
11 | 10 | opelopab2a 4238 | . . 3 |
12 | 9, 11 | syl5bb 191 | . 2 |
13 | 6, 12 | biadan2 452 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wcel 2135 cop 3574 class class class wbr 3977 copab 4037 cxp 4597 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4095 ax-pow 4148 ax-pr 4182 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2724 df-un 3116 df-in 3118 df-ss 3125 df-pw 3556 df-sn 3577 df-pr 3578 df-op 3580 df-br 3978 df-opab 4039 df-xp 4605 |
This theorem is referenced by: lmbr 12780 |
Copyright terms: Public domain | W3C validator |