Theorem adantrll

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

	Ref	Expression
Hypothesis	adantr2.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
Assertion	adantrll	⊢ ( ( 𝜑 ∧ ( ( 𝜏 ∧ 𝜓 ) ∧ 𝜒 ) ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		adantr2.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
2		simpr	⊢ ( ( 𝜏 ∧ 𝜓 ) → 𝜓 )
3	2 1	sylanr1	⊢ ( ( 𝜑 ∧ ( ( 𝜏 ∧ 𝜓 ) ∧ 𝜒 ) ) → 𝜃 )