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Theorem resolution 45270
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 488 . 2 ((𝜑𝜓) → 𝜓)
2 simpr 488 . 2 ((¬ 𝜑𝜒) → 𝜒)
31, 2orim12i 906 1 (((𝜑𝜓) ∨ (¬ 𝜑𝜒)) → (𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 399  wo 844
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  df-or 845
This theorem is referenced by: (None)
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