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Metamath Proof Explorer

Theorem simprd

Description: Deduction eliminating a conjunct. (Contributed by NM, 14-May-1993) A translation of natural deduction rule /\ ER ( /\ elimination right), see natded . (Proof shortened by Wolf Lammen, 3-Oct-2013)

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

Proof

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