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Mirrors > Home > MPE Home > Th. List > Mathboxes > 2alanimi | Structured version Visualization version GIF version |
Description: Removes two universal quantifiers from a statement. (Contributed by Andrew Salmon, 24-May-2011.) |
Ref | Expression |
---|---|
2alanimi.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
2alanimi | ⊢ ((∀𝑥∀𝑦𝜑 ∧ ∀𝑥∀𝑦𝜓) → ∀𝑥∀𝑦𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2alanimi.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
2 | 1 | alanimi 1823 | . 2 ⊢ ((∀𝑦𝜑 ∧ ∀𝑦𝜓) → ∀𝑦𝜒) |
3 | 2 | alanimi 1823 | 1 ⊢ ((∀𝑥∀𝑦𝜑 ∧ ∀𝑥∀𝑦𝜓) → ∀𝑥∀𝑦𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 ∀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 |
This theorem depends on definitions: df-bi 206 df-an 397 |
This theorem is referenced by: (None) |
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