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Mirrors > Home > ILE Home > Th. List > rspcedvd | Unicode version |
Description: Restricted existential specialization, using implicit substitution. Variant of rspcedv 2793. (Contributed by AV, 27-Nov-2019.) |
Ref | Expression |
---|---|
rspcedvd.1 | |
rspcedvd.2 | |
rspcedvd.3 |
Ref | Expression |
---|---|
rspcedvd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspcedvd.3 | . 2 | |
2 | rspcedvd.1 | . . 3 | |
3 | rspcedvd.2 | . . 3 | |
4 | 2, 3 | rspcedv 2793 | . 2 |
5 | 1, 4 | mpd 13 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 wrex 2417 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-v 2688 |
This theorem is referenced by: rspcime 2796 rspcedeq1vd 2798 rspcedeq2vd 2799 updjud 6967 modqmuladd 10139 modqmuladdnn0 10141 modfzo0difsn 10168 negfi 10999 divconjdvds 11547 2tp1odd 11581 dfgcd2 11702 qredeu 11778 pw2dvdslemn 11843 xmettx 12679 |
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