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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 1827 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | ax-5 1827 | . 2 ⊢ (𝜓 → ∀𝑥𝜓) | |
3 | bnj1350.1 | . 2 ⊢ (𝜒 → ∀𝑥𝜒) | |
4 | 1, 2, 3 | hb3an 2114 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → ∀𝑥(𝜑 ∧ 𝜓 ∧ 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1031 ∀wal 1473 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 |
This theorem is referenced by: bnj911 30256 bnj1093 30302 |
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