Description: "At most one" remains true inside ordered pair quantification. (Contributed by NM, 28-May-1995)
Ref | Expression | ||
---|---|---|---|
Hypothesis | mosubop.1 | |- E* x ph |
|
Assertion | mosubop | |- E* x E. y E. z ( A = <. y , z >. /\ ph ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mosubop.1 | |- E* x ph |
|
2 | 1 | gen2 | |- A. y A. z E* x ph |
3 | mosubopt | |- ( A. y A. z E* x ph -> E* x E. y E. z ( A = <. y , z >. /\ ph ) ) |
|
4 | 2 3 | ax-mp | |- E* x E. y E. z ( A = <. y , z >. /\ ph ) |