Prove
1∀x (P(x) → Q(x))
2∀x (Q(x) → R(x))
⊢∀x (P(x) → R(x))
All Ps are Qs and all Qs are Rs, so all Ps are Rs (the syllogism Barbara).
How to write a proof
- Type formulas with the symbol bar or ASCII: ~ ¬, & ∧, | ∨, -> →, <-> ↔, # ⊥, Ax ∀x, Ex ∃x.
- Enter adds a line, ⌘/Ctrl+Enter opens a subproof, Shift+Enter ends one.
- Cite lines like 1, 3 and subproofs like 2-5.
- For ∀I and ∃E, start the subproof with a boxed constant: [c] or [c] P(c).
Proof
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