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Mirrors > Home > MPE Home > Th. List > opabbid | Structured version Visualization version Unicode version |
Description: Equivalent wff's yield equal ordered-pair class abstractions (deduction rule). (Contributed by NM, 21-Feb-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
opabbid.1 | |
opabbid.2 | |
opabbid.3 |
Ref | Expression |
---|---|
opabbid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opabbid.1 | . . . 4 | |
2 | opabbid.2 | . . . . 5 | |
3 | opabbid.3 | . . . . . 6 | |
4 | 3 | anbi2d 740 | . . . . 5 |
5 | 2, 4 | exbid 2091 | . . . 4 |
6 | 1, 5 | exbid 2091 | . . 3 |
7 | 6 | abbidv 2741 | . 2 |
8 | df-opab 4713 | . 2 | |
9 | df-opab 4713 | . 2 | |
10 | 7, 8, 9 | 3eqtr4g 2681 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wex 1704 wnf 1708 cab 2608 cop 4183 copab 4712 |
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 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-opab 4713 |
This theorem is referenced by: opabbidv 4716 mpteq12f 4731 mpteq12d 4734 mpteq12df 4735 feqmptdf 6251 fnoprabg 6761 sprsymrelfo 41747 |
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