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Theorem ex-natded5.7-2 27399
 Description: A more efficient proof of Theorem 5.7 of [Clemente] p. 19. Compare with ex-natded5.7 27398. (Contributed by Mario Carneiro, 9-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ex-natded5.7.1 (𝜑 → (𝜓 ∨ (𝜒𝜃)))
Assertion
Ref Expression
ex-natded5.7-2 (𝜑 → (𝜓𝜒))

Proof of Theorem ex-natded5.7-2
StepHypRef Expression
1 ex-natded5.7.1 . 2 (𝜑 → (𝜓 ∨ (𝜒𝜃)))
2 simpl 472 . . 3 ((𝜒𝜃) → 𝜒)
32orim2i 539 . 2 ((𝜓 ∨ (𝜒𝜃)) → (𝜓𝜒))
41, 3syl 17 1 (𝜑 → (𝜓𝜒))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ wo 382   ∧ 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 197  df-or 384  df-an 385 This theorem is referenced by: (None)
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