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Mirrors > Home > ILE Home > Th. List > rspceeqv | Unicode version |
Description: Restricted existential specialization in an equality, using implicit substitution. (Contributed by BJ, 2-Sep-2022.) |
Ref | Expression |
---|---|
rspceeqv.1 |
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Ref | Expression |
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rspceeqv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspceeqv.1 |
. . 3
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2 | 1 | eqeq2d 2189 |
. 2
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3 | 2 | rspcev 2841 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-v 2739 |
This theorem is referenced by: elixpsn 6732 ixpsnf1o 6733 elfir 6969 0ct 7103 ctmlemr 7104 ctssdclemn0 7106 fodju0 7142 mertenslemi1 11536 mertenslem2 11537 pcprmpw 12325 1arithlem4 12356 ctiunctlemfo 12432 elrestr 12684 restopnb 13552 mopnex 13876 metrest 13877 2sqlem2 14322 mul2sq 14323 2sqlem3 14324 2sqlem9 14331 2sqlem10 14332 |
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