Theorem simpld

Description: Deduction eliminating a conjunct. A translation of natural deduction rule /\ EL ( /\ elimination left), see natded . (Contributed by NM, 26-May-1993)

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

Proof

Step	Hyp	Ref	Expression
1		simpld.1	⊢ ( 𝜑 → ( 𝜓 ∧ 𝜒 ) )
2		simpl	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜓 )
3	1 2	syl	⊢ ( 𝜑 → 𝜓 )