Description: Equality theorem for restricted existential quantifier. (Contributed by NM, 29-Oct-1995) Remove usage of ax-10 , ax-11 , and ax-12 . (Revised by Steven Nguyen, 30-Apr-2023) Shorten other proofs. (Revised by Wolf Lammen, 8-Mar-2025)
Ref | Expression | ||
---|---|---|---|
Assertion | rexeq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfcleq | ||
2 | anbi1 | ||
3 | 2 | alexbii | |
4 | 1 3 | sylbi | |
5 | df-rex | ||
6 | df-rex | ||
7 | 4 5 6 | 3bitr4g |