![]() |
Mathbox for Jonathan Ben-Naim |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1350 | Structured version Visualization version GIF version |
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj1350.1 | ⊢ (𝜒 → ∀𝑥𝜒) |
Ref | Expression |
---|---|
bnj1350 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → ∀𝑥(𝜑 ∧ 𝜓 ∧ 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-5 1905 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | ax-5 1905 | . 2 ⊢ (𝜓 → ∀𝑥𝜓) | |
3 | bnj1350.1 | . 2 ⊢ (𝜒 → ∀𝑥𝜒) | |
4 | 1, 2, 3 | hb3an 2289 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → ∀𝑥(𝜑 ∧ 𝜓 ∧ 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1084 ∀wal 1531 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-10 2129 ax-12 2163 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-3an 1086 df-tru 1536 df-ex 1774 df-nf 1778 |
This theorem is referenced by: bnj911 34472 bnj1093 34520 |
Copyright terms: Public domain | W3C validator |