Description: A commutation rule for distinct variable specifiers. Version of naecoms using ax-c11 . (Contributed by NM, 2-Jan-2002) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | nalequcoms-o.1 | |- ( -. A. x x = y -> ph ) |
|
| Assertion | naecoms-o | |- ( -. A. y y = x -> ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nalequcoms-o.1 | |- ( -. A. x x = y -> ph ) |
|
| 2 | aecom-o | |- ( A. x x = y -> A. y y = x ) |
|
| 3 | 2 1 | nsyl4 | |- ( -. ph -> A. y y = x ) |
| 4 | 3 | con1i | |- ( -. A. y y = x -> ph ) |