Theorem looinv 77

Description: The Inversion Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. Using dfor2 199, we can see that this essentially expresses "disjunction commutes." Theorem *2.69 of [WhiteheadRussell] p. 108.

Assertion

Ref	Expression
looinv	⊢ (((φ → ψ) → ψ) → ((ψ → φ) → φ))

Proof of Theorem looinv

Step	Hyp	Ref	Expression
1		syl2 17	. 2 ⊢ (((φ → ψ) → ψ) → ((ψ → φ) → ((φ → ψ) → φ)))
2		peirce 76	. 2 ⊢ (((φ → ψ) → φ) → φ)
3	1, 2	syl6 23	1 ⊢ (((φ → ψ) → ψ) → ((ψ → φ) → φ))

Syntax hints:   → wi 2

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

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