Theorem adantrlr 755

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
adantrlr	⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜏) ∧ 𝜒)) → 𝜃)

Proof of Theorem adantrlr

Step	Hyp	Ref	Expression
1		simpl 472	. 2 ⊢ ((𝜓 ∧ 𝜏) → 𝜓)
2		adantr2.1	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	1, 2	sylanr1 682	1 ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜏) ∧ 𝜒)) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 383

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 196  df-an 385

This theorem is referenced by:  smoord  7349  addsrmo  9773  mulsrmo  9774  lediv12a  10795  nrmmetd  22189  pntrmax  25053  ablo4  26788  mdslmd3i  28575  atom1d  28596  esumiun  29483  poimirlem28  32607  fdc  32711  incsequz  32714  crngm4  32972  ps-2  33782  aacllem  42356