Theorem adantrrl 723

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 486	. 2 ⊢ ((𝜏 ∧ 𝜒) → 𝜒)
2		adantr2.1	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	1, 2	sylanr2 682	1 ⊢ ((𝜑 ∧ (𝜓 ∧ (𝜏 ∧ 𝜒))) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 397

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 398

This theorem is referenced by:  zorn2lem6  10492  ltmul12a  12066  mndind  18705  neiint  22590  neissex  22613  1stcfb  22931  1stcrest  22939  grporcan  29749  mdslmd3i  31563  colineardim1  34971  cvratlem  38230  ps-2  38287  fsuppssind  41115