Description: Interchange class substitution and restricted unique existential quantifier. (Contributed by NM, 24-Feb-2013) (Revised by NM, 18-Aug-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | sbcreu | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcex | |
|
2 | reurex | |
|
3 | sbcex | |
|
4 | 3 | rexlimivw | |
5 | 2 4 | syl | |
6 | dfsbcq2 | |
|
7 | dfsbcq2 | |
|
8 | 7 | reubidv | |
9 | nfcv | |
|
10 | nfs1v | |
|
11 | 9 10 | nfreuw | |
12 | sbequ12 | |
|
13 | 12 | reubidv | |
14 | 11 13 | sbiev | |
15 | 6 8 14 | vtoclbg | |
16 | 1 5 15 | pm5.21nii | |