Theorem adantrrl 455

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
adantrrl	⊢ ((𝜑 ∧ (𝜓 ∧ (𝜏 ∧ 𝜒))) → 𝜃)

Proof of Theorem adantrrl

Step	Hyp	Ref	Expression
1		simpr 103	. 2 ⊢ ((𝜏 ∧ 𝜒) → 𝜒)
2		adantr2.1	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	1, 2	sylanr2 385	1 ⊢ ((𝜑 ∧ (𝜓 ∧ (𝜏 ∧ 𝜒))) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem is referenced by:  1stconst  5842  ltexprlemdisj  6704  ltmul12a  7826