Theorem pm5.4 351

Description: Antecedent absorption implication. Theorem *5.4 of [WhiteheadRussell] p. 125. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem pm5.4

Step	Hyp	Ref	Expression
1		pm2.43 47	. 2 ⊢ ((φ → (φ → ψ)) → (φ → ψ))
2		ax-1 6	. 2 ⊢ ((φ → ψ) → (φ → (φ → ψ)))
3	1, 2	impbii 180	1 ⊢ ((φ → (φ → ψ)) ↔ (φ → ψ))

Syntax hints:   → wi 4   ↔ wb 176

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  moabs  2248