Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-19.21bit | Structured version Visualization version GIF version |
Description: Closed form of 19.21bi 2186. (Contributed by BJ, 20-Oct-2019.) |
Ref | Expression |
---|---|
bj-19.21bit | ⊢ ((𝜑 → ∀𝑥𝜓) → (𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sp 2180 | . 2 ⊢ (∀𝑥𝜓 → 𝜓) | |
2 | 1 | imim2i 16 | 1 ⊢ ((𝜑 → ∀𝑥𝜓) → (𝜑 → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2015 ax-12 2175 |
This theorem depends on definitions: df-bi 206 df-ex 1787 |
This theorem is referenced by: bj-wnfenf 34890 bj-dfnnf3 34927 |
Copyright terms: Public domain | W3C validator |