Theorem adantrll 476

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

Hypothesis

Ref	Expression
adantr2.1	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)

Assertion

Ref	Expression
adantrll	⊢ ((𝜑 ∧ ((𝜏 ∧ 𝜓) ∧ 𝜒)) → 𝜃)

Proof of Theorem adantrll

Step	Hyp	Ref	Expression
1		simpr 109	. 2 ⊢ ((𝜏 ∧ 𝜓) → 𝜓)
2		adantr2.1	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	1, 2	sylanr1 402	1 ⊢ ((𝜑 ∧ ((𝜏 ∧ 𝜓) ∧ 𝜒)) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by:  ltexprlemdisj  7547