Theorem 3anidm23

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

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

Proof

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