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Metamath Proof Explorer

Theorem xor2

Description: Two ways to express "exclusive or". (Contributed by Mario Carneiro, 4-Sep-2016)

Ref Expression
Assertion xor2 ⊢ φ ⊻ ψ ↔ φ ∨ ψ ∧ ¬ φ ∧ ψ

Proof

Step Hyp Ref Expression
1 df-xor ⊢ φ ⊻ ψ ↔ ¬ φ ↔ ψ
2 nbi2 ⊢ ¬ φ ↔ ψ ↔ φ ∨ ψ ∧ ¬ φ ∧ ψ
3 1 2 bitri ⊢ φ ⊻ ψ ↔ φ ∨ ψ ∧ ¬ φ ∧ ψ