Description: If A. x ph is affirmed, ph cannot be denied. Identical to sp . See ax-frege58b and frege58c for versions which more closely track the original. Axiom 58 of Frege1879 p. 51. (Contributed by RP, 28-Mar-2020) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | frege58bid | |- ( A. x ph -> ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-frege58b | |- ( A. x ph -> [ x / x ] ph ) |
|
| 2 | sbid | |- ( [ x / x ] ph <-> ph ) |
|
| 3 | 2 | biimpi | |- ( [ x / x ] ph -> ph ) |
| 4 | 1 3 | syl | |- ( A. x ph -> ph ) |