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Theorem simprld 790
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 477 . 2 (𝜑 → (𝜒𝜃))
32simpld 473 1 (𝜑𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
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 195  df-an 384
This theorem is referenced by:  evlssca  19291  dfcgra2  25466  lbioc  38369  icccncfext  38556  stoweidlem37  38713  fourierdlem41  38824  fourierdlem48  38830  fourierdlem49  38831  fourierdlem74  38856  fourierdlem75  38857  salgencl  39009  salgenuni  39014  issalgend  39015  smfaddlem1  39432
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