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

Theorem simprld 791
 Description: Deduction eliminating a double conjunct. (Contributed by Glauco Siliprandi, 11-Dec-2019.)
Hypothesis
Ref Expression
simprld.1 (𝜑 → (𝜓 ∧ (𝜒𝜃)))
Assertion
Ref Expression
simprld (𝜑𝜒)

Proof of Theorem simprld
StepHypRef Expression
1 simprld.1 . . 3 (𝜑 → (𝜓 ∧ (𝜒𝜃)))
21simprd 478 . 2 (𝜑 → (𝜒𝜃))
32simpld 474 1 (𝜑𝜒)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383 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 196  df-an 385 This theorem is referenced by:  evlssca  19343  dfcgra2  25521  lbioc  38586  icccncfext  38773  stoweidlem37  38930  fourierdlem41  39041  fourierdlem48  39047  fourierdlem49  39048  fourierdlem74  39073  fourierdlem75  39074  salgencl  39226  salgenuni  39231  issalgend  39232  smfaddlem1  39649
 Copyright terms: Public domain W3C validator