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Mirrors > Home > ILE Home > Th. List > copsex4g | Unicode version |
Description: An implicit substitution inference for 2 ordered pairs. (Contributed by NM, 5-Aug-1995.) |
Ref | Expression |
---|---|
copsex4g.1 |
Ref | Expression |
---|---|
copsex4g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqcom 2139 | . . . . . . 7 | |
2 | vex 2684 | . . . . . . . 8 | |
3 | vex 2684 | . . . . . . . 8 | |
4 | 2, 3 | opth 4154 | . . . . . . 7 |
5 | 1, 4 | bitri 183 | . . . . . 6 |
6 | eqcom 2139 | . . . . . . 7 | |
7 | vex 2684 | . . . . . . . 8 | |
8 | vex 2684 | . . . . . . . 8 | |
9 | 7, 8 | opth 4154 | . . . . . . 7 |
10 | 6, 9 | bitri 183 | . . . . . 6 |
11 | 5, 10 | anbi12i 455 | . . . . 5 |
12 | 11 | anbi1i 453 | . . . 4 |
13 | 12 | a1i 9 | . . 3 |
14 | 13 | 4exbidv 1842 | . 2 |
15 | id 19 | . . 3 | |
16 | copsex4g.1 | . . 3 | |
17 | 15, 16 | cgsex4g 2718 | . 2 |
18 | 14, 17 | bitrd 187 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wex 1468 wcel 1480 cop 3525 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 |
This theorem is referenced by: opbrop 4613 ovi3 5900 dfplpq2 7155 dfmpq2 7156 enq0breq 7237 |
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