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34. Proof by Cases

MediumPropositional
Prove
1P → R
2Q → R
⊢(P ∨ Q) → R

If R follows from P and also from Q, it follows from P ∨ Q.

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).
Full rule reference ↗

Proof

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