Theorem adantrlr 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
adantrlr	⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜏) ∧ 𝜒)) → 𝜃)

Proof of Theorem adantrlr

Step	Hyp	Ref	Expression
1		simpl 482	. 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 395

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 207  df-an 396

This theorem is referenced by:  smoord  8295  addsrmo  10986  mulsrmo  10987  lediv12a  12036  nrmmetd  24478  pntrmax  27491  ablo4  30512  mdslmd3i  32294  atom1d  32315  fsumiunle  32787  esumiun  34063  poimirlem28  37630  fdc  37727  incsequz  37730  crngm4  37985  ps-2  39460  aacllem  49790