Mathbox for Richard Penner |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > ax-frege58b | Structured version Visualization version GIF version |
Description: If ∀𝑥𝜑 is affirmed, [𝑦 / 𝑥]𝜑 cannot be denied. Identical to stdpc4 2071. Axiom 58 of [Frege1879] p. 51. (Contributed by RP, 28-Mar-2020.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ax-frege58b | ⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . 3 wff 𝜑 | |
2 | vx | . . 3 setvar 𝑥 | |
3 | 1, 2 | wal 1537 | . 2 wff ∀𝑥𝜑 |
4 | vy | . . 3 setvar 𝑦 | |
5 | 1, 2, 4 | wsb 2067 | . 2 wff [𝑦 / 𝑥]𝜑 |
6 | 3, 5 | wi 4 | 1 wff (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑) |
Colors of variables: wff setvar class |
This axiom is referenced by: frege58bid 41480 frege58bcor 41481 frege60b 41483 frege61b 41484 frege67b 41490 frege58c 41499 |
Copyright terms: Public domain | W3C validator |