Prove
1∃x (P(x) ∧ Q(x))
⊢∃x P(x) ∧ ∃x Q(x)
If something is both P and Q, then something is P and something is Q. (The converse fails!)
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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