Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > resoprab2 | Unicode version |
Description: Restriction of an operator abstraction. (Contributed by Jeff Madsen, 2-Sep-2009.) |
Ref | Expression |
---|---|
resoprab2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resoprab 5949 | . 2 | |
2 | anass 399 | . . . 4 | |
3 | an4 581 | . . . . . 6 | |
4 | ssel 3141 | . . . . . . . . 9 | |
5 | 4 | pm4.71d 391 | . . . . . . . 8 |
6 | 5 | bicomd 140 | . . . . . . 7 |
7 | ssel 3141 | . . . . . . . . 9 | |
8 | 7 | pm4.71d 391 | . . . . . . . 8 |
9 | 8 | bicomd 140 | . . . . . . 7 |
10 | 6, 9 | bi2anan9 601 | . . . . . 6 |
11 | 3, 10 | syl5bb 191 | . . . . 5 |
12 | 11 | anbi1d 462 | . . . 4 |
13 | 2, 12 | bitr3id 193 | . . 3 |
14 | 13 | oprabbidv 5907 | . 2 |
15 | 1, 14 | eqtrid 2215 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wcel 2141 wss 3121 cxp 4609 cres 4613 coprab 5854 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-opab 4051 df-xp 4617 df-rel 4618 df-res 4623 df-oprab 5857 |
This theorem is referenced by: resmpo 5951 |
Copyright terms: Public domain | W3C validator |