Prove
1∃x (P(x) ∧ ∀y (P(y) → (y = x)))
2P(a)
3P(b)
⊢a = b
Exactly one thing is a P. So if a and b are both Ps, they're the same object.
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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