Theorem anidmdbi 627

Description: Conjunction idempotence with antecedent. (Contributed by Roy F. Longton, 8-Aug-2005.)

Assertion

Ref	Expression
anidmdbi	⊢ ((φ → (ψ ∧ ψ)) ↔ (φ → ψ))

Proof of Theorem anidmdbi

Step	Hyp	Ref	Expression
1		anidm 625	. 2 ⊢ ((ψ ∧ ψ) ↔ ψ)
2	1	imbi2i 303	1 ⊢ ((φ → (ψ ∧ ψ)) ↔ (φ → ψ))

Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358

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  df-an 360

This theorem is referenced by:  nanim  1292