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Mirrors > Home > ILE Home > Th. List > rabeqbidv | Unicode version |
Description: Equality of restricted class abstractions. (Contributed by Jeff Madsen, 1-Dec-2009.) |
Ref | Expression |
---|---|
rabeqbidv.1 | |
rabeqbidv.2 |
Ref | Expression |
---|---|
rabeqbidv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rabeqbidv.1 | . . 3 | |
2 | rabeq 2713 | . . 3 | |
3 | 1, 2 | syl 14 | . 2 |
4 | rabeqbidv.2 | . . 3 | |
5 | 4 | rabbidv 2710 | . 2 |
6 | 3, 5 | eqtrd 2197 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1342 crab 2446 |
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-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rab 2451 |
This theorem is referenced by: elfvmptrab1 5574 mpoxopoveq 6199 supeq123d 6947 phival 12122 dfphi2 12129 cldval 12640 neifval 12681 cnfval 12735 cnpfval 12736 cnprcl2k 12747 hmeofvalg 12844 ispsmet 12864 ismet 12885 isxmet 12886 blfvalps 12926 cncfval 13100 |
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