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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 1918 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | bnj1352.1 | . 2 ⊢ (𝜓 → ∀𝑥𝜓) | |
3 | 1, 2 | hban 2302 | 1 ⊢ ((𝜑 ∧ 𝜓) → ∀𝑥(𝜑 ∧ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 ∀wal 1541 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-10 2142 ax-12 2176 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-tru 1546 df-ex 1788 df-nf 1792 |
This theorem is referenced by: bnj594 32631 bnj1309 32741 |
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