Theorem adantrlr 735

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 487	. 2 ⊢ ((𝜓 ∧ 𝜏) → 𝜓)
2		adantr2.1	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	1, 2	sylanr1 694	1 ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜏) ∧ 𝜒)) → 𝜃)

This proof depends on syntax axioms:   → wi 4   ∧ wa 400

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401

This theorem is used by:  smoord  8348  addsrmo  11062  mulsrmo  11063  lediv12a  12112  nrmmetd  24740  pntrmax  27737  ablo4  30911  mdslmd3i  32693  atom1d  32714  fsumiunle  33182  esumiun  34493  poimirlem28  38327  fdc  38424  incsequz  38427  crngm4  38682  ps-2  40280  aacllem  50649