Description: Alternate proof of stdpc4 , shorter but using additional axioms. (Contributed by WL, 5-Jun-2026) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | stdpc4ALT | |- ( A. x ph -> [ t / x ] ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ala1 | |- ( A. x ph -> A. x ( x = y -> ph ) ) |
|
| 2 | 1 | a1d | |- ( A. x ph -> ( y = t -> A. x ( x = y -> ph ) ) ) |
| 3 | 2 | alrimiv | |- ( A. x ph -> A. y ( y = t -> A. x ( x = y -> ph ) ) ) |
| 4 | dfsb | |- ( [ t / x ] ph <-> A. y ( y = t -> A. x ( x = y -> ph ) ) ) |
|
| 5 | 3 4 | sylibr | |- ( A. x ph -> [ t / x ] ph ) |