Theorem adantllr

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004) (Proof shortened by Wolf Lammen, 4-Dec-2012)

	Ref	Expression
Hypothesis	adantl2.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
Assertion	adantllr	⊢ ( ( ( ( 𝜑 ∧ 𝜏 ) ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		adantl2.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
2		simpl	⊢ ( ( 𝜑 ∧ 𝜏 ) → 𝜑 )
3	2 1	sylanl1	⊢ ( ( ( ( 𝜑 ∧ 𝜏 ) ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )