Theorem pm5.4 146

Description: Antecedent absorption implication. Theorem *5.4 of [WhiteheadRussell] p. 125.

Assertion

Ref	Expression
pm5.4	⊢ ((φ → (φ → ψ)) ↔ (φ → ψ))

Proof of Theorem pm5.4

Step	Hyp	Ref	Expression
1		pm2.43 57	. 2 ⊢ ((φ → (φ → ψ)) → (φ → ψ))
2		ax-1 3	. 2 ⊢ ((φ → ψ) → (φ → (φ → ψ)))
3	1, 2	impbi 139	1 ⊢ ((φ → (φ → ψ)) ↔ (φ → ψ))

Syntax hints:   → wi 2   ↔ wb 127

This theorem is referenced by:  moabs 1041

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

This theorem depends on definitions:  df-bi 128

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