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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 |
Ref | Expression |
---|---|
rspceeqv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspceeqv.1 | . . 3 | |
2 | 1 | eqeq2d 2176 | . 2 |
3 | 2 | rspcev 2825 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 wcel 2135 wrex 2443 |
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-rex 2448 df-v 2723 |
This theorem is referenced by: elixpsn 6692 ixpsnf1o 6693 elfir 6929 0ct 7063 ctmlemr 7064 ctssdclemn0 7066 fodju0 7102 mertenslemi1 11462 mertenslem2 11463 pcprmpw 12244 ctiunctlemfo 12315 elrestr 12506 restopnb 12728 mopnex 13052 metrest 13053 |
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