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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1352 | 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 |
---|---|
bnj1352.1 | ⊢ (𝜓 → ∀𝑥𝜓) |
Ref | Expression |
---|---|
bnj1352 | ⊢ ((𝜑 ∧ 𝜓) → ∀𝑥(𝜑 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-5 1902 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | bnj1352.1 | . 2 ⊢ (𝜓 → ∀𝑥𝜓) | |
3 | 1, 2 | hban 2299 | 1 ⊢ ((𝜑 ∧ 𝜓) → ∀𝑥(𝜑 ∧ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 ∀wal 1526 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-10 2136 ax-12 2167 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 |
This theorem is referenced by: bnj594 32083 bnj1309 32191 |
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