Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  adantrrl Structured version   Visualization version   GIF version

 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 ∧ (𝜓𝜒)) → 𝜃)
Assertion
Ref Expression
adantrrl ((𝜑 ∧ (𝜓 ∧ (𝜏𝜒))) → 𝜃)

Proof of Theorem adantrrl
StepHypRef Expression
1 simpr 488 . 2 ((𝜏𝜒) → 𝜒)
2 adantr2.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylanr2 682 1 ((𝜑 ∧ (𝜓 ∧ (𝜏𝜒))) → 𝜃)
 Colors of variables: wff setvar class 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 210  df-an 400 This theorem is referenced by:  zorn2lem6  9919  ltmul12a  11492  mndind  17991  neiint  21723  neissex  21746  1stcfb  22064  1stcrest  22072  grporcan  28315  mdslmd3i  30129  colineardim1  33671  cvratlem  36757  ps-2  36814  fsuppssind  39520
 Copyright terms: Public domain W3C validator