Theorem adantl

Description: Inference adding a conjunct to the left of an antecedent. (Contributed by NM, 30-Aug-1993) (Proof shortened by Wolf Lammen, 23-Nov-2012)

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

Proof

Step	Hyp	Ref	Expression
1		adantl.1	⊢ ( 𝜑 → 𝜓 )
2	1	adantr	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜓 )
3	2	ancoms	⊢ ( ( 𝜒 ∧ 𝜑 ) → 𝜓 )