Description: Elimination of an existential quantifier, using implicit substitution. (Contributed by NM, 2-Mar-1995)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ceqsexv.1 | |- A e. _V |
|
ceqsexv.2 | |- ( x = A -> ( ph <-> ps ) ) |
||
Assertion | ceqsexv | |- ( E. x ( x = A /\ ph ) <-> ps ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ceqsexv.1 | |- A e. _V |
|
2 | ceqsexv.2 | |- ( x = A -> ( ph <-> ps ) ) |
|
3 | nfv | |- F/ x ps |
|
4 | 3 1 2 | ceqsex | |- ( E. x ( x = A /\ ph ) <-> ps ) |