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26. Indiscernibility of Identicals

EasyIdentity
Prove
1P(a)
2a = b
⊢P(b)

If a and b are the same object, whatever is true of a is true of b.

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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