Theorem adantrlr 736

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 488	. 2 ⊢ ((𝜓 ∧ 𝜏) → 𝜓)
2		adantr2.1	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	1, 2	sylanr1 695	1 ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜏) ∧ 𝜒)) → 𝜃)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

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 402

This theorem is used by:  smoord  8354  addsrmo  11082  mulsrmo  11083  lediv12a  12132  nrmmetd  24800  pntrmax  27800  ablo4  31031  mdslmd3i  32813  atom1d  32834  fsumiunle  33299  esumiun  34604  poimirlem28  38397  fdc  38495  incsequz  38498  crngm4  38753  ps-2  40351  aacllem  50772