Theorem ad2antll

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 19-Oct-1999)

	Ref	Expression
Hypothesis	ad2ant.1	⊢ ( 𝜑 → 𝜓 )
Assertion	ad2antll	⊢ ( ( 𝜒 ∧ ( 𝜃 ∧ 𝜑 ) ) → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		ad2ant.1	⊢ ( 𝜑 → 𝜓 )
2	1	adantl	⊢ ( ( 𝜃 ∧ 𝜑 ) → 𝜓 )
3	2	adantl	⊢ ( ( 𝜒 ∧ ( 𝜃 ∧ 𝜑 ) ) → 𝜓 )