Description: If A. x ph is affirmed, [ y / x ] ph cannot be denied. Identical to stdpc4 . Axiom 58 of Frege1879 p. 51. (Contributed by RP, 28-Mar-2020) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ax-frege58b | |- ( A. x ph -> [ y / x ] ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 0 | vx | |- x |
|
| 1 | wph | |- ph |
|
| 2 | 1 0 | wal | |- A. x ph |
| 3 | vy | |- y |
|
| 4 | 1 0 3 | wsb | |- [ y / x ] ph |
| 5 | 2 4 | wi | |- ( A. x ph -> [ y / x ] ph ) |