Theorem 3anidm12

Description: Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008)

	Ref	Expression
Hypothesis	3anidm12.1	⊢ ( ( 𝜑 ∧ 𝜑 ∧ 𝜓 ) → 𝜒 )
Assertion	3anidm12	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		3anidm12.1	⊢ ( ( 𝜑 ∧ 𝜑 ∧ 𝜓 ) → 𝜒 )
2	1	3expib	⊢ ( 𝜑 → ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) )
3	2	anabsi5	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )