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Theorem resolution 41874
Description: Resolution rule. This is the primary inference rule in some automated theorem provers such as prover9. The resolution rule can be traced back to Davis and Putnam (1960). (Contributed by David A. Wheeler, 9-Feb-2017.)
Assertion
Ref Expression
resolution (((𝜑𝜓) ∨ (¬ 𝜑𝜒)) → (𝜓𝜒))

Proof of Theorem resolution
StepHypRef Expression
1 simpr 477 . 2 ((𝜑𝜓) → 𝜓)
2 simpr 477 . 2 ((¬ 𝜑𝜒) → 𝜒)
31, 2orim12i 538 1 (((𝜑𝜓) ∨ (¬ 𝜑𝜒)) → (𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 383  wa 384
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 197  df-or 385  df-an 386
This theorem is referenced by: (None)
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