Description: Membership in a class abstraction, using implicit substitution. Compare Theorem 6.13 of Quine p. 44. (Contributed by NM, 1-Aug-1994)
Ref | Expression | ||
---|---|---|---|
Hypotheses | elab.1 | |- A e. _V |
|
elab.2 | |- ( x = A -> ( ph <-> ps ) ) |
||
Assertion | elab | |- ( A e. { x | ph } <-> ps ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elab.1 | |- A e. _V |
|
2 | elab.2 | |- ( x = A -> ( ph <-> ps ) ) |
|
3 | nfv | |- F/ x ps |
|
4 | 3 1 2 | elabf | |- ( A e. { x | ph } <-> ps ) |