![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > spvw | Structured version Visualization version GIF version |
Description: Version of sp 2167 when 𝑥 does not occur in 𝜑. Converse of ax-5 1953. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 10-Apr-2017.) (Proof shortened by Wolf Lammen, 4-Dec-2017.) |
Ref | Expression |
---|---|
spvw | ⊢ (∀𝑥𝜑 → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.3v 2031 | . 2 ⊢ (∀𝑥𝜑 ↔ 𝜑) | |
2 | 1 | biimpi 208 | 1 ⊢ (∀𝑥𝜑 → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1599 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 |
This theorem depends on definitions: df-bi 199 df-ex 1824 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |