Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > sptruw | Structured version Visualization version GIF version |
Description: Version of sp 2180 when 𝜑 is true. Instance of a1i 11. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 23-Apr-2017.) |
Ref | Expression |
---|---|
sptruw.1 | ⊢ 𝜑 |
Ref | Expression |
---|---|
sptruw | ⊢ (∀𝑥𝜑 → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sptruw.1 | . 2 ⊢ 𝜑 | |
2 | 1 | a1i 11 | 1 ⊢ (∀𝑥𝜑 → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |