New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > oprabbid | Unicode version |
Description: Equivalent wff's yield equal operation class abstractions (deduction rule). (Contributed by NM, 21-Feb-2004.) (Revised by Mario Carneiro, 24-Jun-2014.) |
Ref | Expression |
---|---|
oprabbid.1 | |
oprabbid.2 | |
oprabbid.3 | |
oprabbid.4 |
Ref | Expression |
---|---|
oprabbid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oprabbid.1 | . . . 4 | |
2 | oprabbid.2 | . . . . 5 | |
3 | oprabbid.3 | . . . . . 6 | |
4 | oprabbid.4 | . . . . . . 7 | |
5 | 4 | anbi2d 684 | . . . . . 6 |
6 | 3, 5 | exbid 1773 | . . . . 5 |
7 | 2, 6 | exbid 1773 | . . . 4 |
8 | 1, 7 | exbid 1773 | . . 3 |
9 | 8 | abbidv 2467 | . 2 |
10 | df-oprab 5528 | . 2 | |
11 | df-oprab 5528 | . 2 | |
12 | 9, 10, 11 | 3eqtr4g 2410 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wex 1541 wnf 1544 wceq 1642 cab 2339 cop 4561 coprab 5527 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-oprab 5528 |
This theorem is referenced by: oprabbidv 5564 mpt2eq123 5661 |
Copyright terms: Public domain | W3C validator |