Description: Alternate proof of bj-ssbid1 , not using sbequ1 . (Contributed by BJ, 22-Dec-2020) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | bj-ssbid1ALT | |- ( ph -> [ x / x ] ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax12v | |- ( x = y -> ( ph -> A. x ( x = y -> ph ) ) ) |
|
| 2 | 1 | equcoms | |- ( y = x -> ( ph -> A. x ( x = y -> ph ) ) ) |
| 3 | 2 | com12 | |- ( ph -> ( y = x -> A. x ( x = y -> ph ) ) ) |
| 4 | 3 | alrimiv | |- ( ph -> A. y ( y = x -> A. x ( x = y -> ph ) ) ) |
| 5 | df-sb | |- ( [ x / x ] ph <-> A. y ( y = x -> A. x ( x = y -> ph ) ) ) |
|
| 6 | 4 5 | sylibr | |- ( ph -> [ x / x ] ph ) |