Theorem ancl

Description: Conjoin antecedent to left of consequent. (Contributed by NM, 15-Aug-1994)

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

Proof

Step	Hyp	Ref	Expression
1		pm3.2	⊢ ( 𝜑 → ( 𝜓 → ( 𝜑 ∧ 𝜓 ) ) )
2	1	a2i	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → ( 𝜑 ∧ 𝜓 ) ) )