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Metamath Proof Explorer

Theorem simpl

Description: Elimination of a conjunct. Theorem *3.26 (Simp) of WhiteheadRussell p. 112. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 14-Jun-2022)

		Ref	Expression
	Assertion	simpl	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝜑 → 𝜑 )
2	1	adantr	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜑 )