Theorem adantrlr 733

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 486	. 2 ⊢ ((𝜓 ∧ 𝜏) → 𝜓)
2		adantr2.1	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	1, 2	sylanr1 692	1 ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜏) ∧ 𝜒)) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 399

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 209  df-an 400

This theorem is referenced by:  smoord  8330  addsrmo  11025  mulsrmo  11026  lediv12a  12079  nrmmetd  24622  pntrmax  27616  ablo4  30710  mdslmd3i  32492  atom1d  32513  fsumiunle  32992  esumiun  34352  poimirlem28  38108  fdc  38205  incsequz  38208  crngm4  38463  ps-2  40063  aacllem  50383