Theorem ad2ant2l

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 8-Jan-2006)

	Ref	Expression
Hypothesis	ad2ant2.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
Assertion	ad2ant2l	⊢ ( ( ( 𝜃 ∧ 𝜑 ) ∧ ( 𝜏 ∧ 𝜓 ) ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		ad2ant2.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
2	1	adantrl	⊢ ( ( 𝜑 ∧ ( 𝜏 ∧ 𝜓 ) ) → 𝜒 )
3	2	adantll	⊢ ( ( ( 𝜃 ∧ 𝜑 ) ∧ ( 𝜏 ∧ 𝜓 ) ) → 𝜒 )