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Mirrors > Home > ILE Home > Th. List > rspcedeq2vd | Unicode version |
Description: Restricted existential specialization, using implicit substitution. Variant of rspcedvd 2822 for equations, in which the right hand side depends on the quantified variable. (Contributed by AV, 24-Dec-2019.) |
Ref | Expression |
---|---|
rspcedeqvd.1 | |
rspcedeqvd.2 |
Ref | Expression |
---|---|
rspcedeq2vd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspcedeqvd.1 | . 2 | |
2 | rspcedeqvd.2 | . . . 4 | |
3 | 2 | eqcomd 2163 | . . 3 |
4 | 3 | eqeq2d 2169 | . 2 |
5 | eqidd 2158 | . 2 | |
6 | 1, 4, 5 | rspcedvd 2822 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wcel 2128 wrex 2436 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-v 2714 |
This theorem is referenced by: (None) |
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