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Theorem onenotinotbothi 39749
 Description: From one negated implication it is not the case its non negated form and a random others are both true. (Contributed by Jarvin Udandy, 11-Sep-2020.)
Hypothesis
Ref Expression
onenotinotbothi.1 ¬ (𝜑𝜓)
Assertion
Ref Expression
onenotinotbothi ¬ ((𝜑𝜓) ∧ (𝜒𝜃))

Proof of Theorem onenotinotbothi
StepHypRef Expression
1 onenotinotbothi.1 . . 3 ¬ (𝜑𝜓)
21orci 404 . 2 (¬ (𝜑𝜓) ∨ ¬ (𝜒𝜃))
3 pm3.14 522 . 2 ((¬ (𝜑𝜓) ∨ ¬ (𝜒𝜃)) → ¬ ((𝜑𝜓) ∧ (𝜒𝜃)))
42, 3ax-mp 5 1 ¬ ((𝜑𝜓) ∧ (𝜒𝜃))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → 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 196  df-or 384  df-an 385 This theorem is referenced by: (None)
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