Theorem 3anidm23 1241

Description: Inference from idempotent law for conjunction. (Contributed by NM, 1-Feb-2007.)

Hypothesis

Ref	Expression
3anidm23.1	⊢ ((φ ∧ ψ ∧ ψ) → χ)

Assertion

Ref	Expression
3anidm23	⊢ ((φ ∧ ψ) → χ)

Proof of Theorem 3anidm23

Step	Hyp	Ref	Expression
1		3anidm23.1	. . 3 ⊢ ((φ ∧ ψ ∧ ψ) → χ)
2	1	3expa 1151	. 2 ⊢ (((φ ∧ ψ) ∧ ψ) → χ)
3	2	anabss3 796	1 ⊢ ((φ ∧ ψ) → χ)

Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934

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  df-3an 936

This theorem is referenced by:  nnpw1ex  4485  sfindbl  4531  pw1fin  6170