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

Proof of Theorem adantrrl

Step	Hyp	Ref	Expression
1		simpr 484	. 2 ⊢ ((𝜏 ∧ 𝜒) → 𝜒)
2		adantr2.1	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	1, 2	sylanr2 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:  zorn2lem6  10570  ltmul12a  12150  mndind  18863  neiint  23133  neissex  23156  1stcfb  23474  1stcrest  23482  grporcan  30550  mdslmd3i  32364  colineardim1  36025  cvratlem  39378  ps-2  39435  fsuppssind  42548