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Theorem mdandyvrx10 39807
 Description: Given the exclusivities set in the hypotheses, there exist a proof where ch, th, ta, et exclude ze, si accordingly. (Contributed by Jarvin Udandy, 7-Sep-2016.)
Hypotheses
Ref Expression
mdandyvrx10.1 (𝜑𝜁)
mdandyvrx10.2 (𝜓𝜎)
mdandyvrx10.3 (𝜒𝜑)
mdandyvrx10.4 (𝜃𝜓)
mdandyvrx10.5 (𝜏𝜑)
mdandyvrx10.6 (𝜂𝜓)
Assertion
Ref Expression
mdandyvrx10 ((((𝜒𝜁) ∧ (𝜃𝜎)) ∧ (𝜏𝜁)) ∧ (𝜂𝜎))

Proof of Theorem mdandyvrx10
StepHypRef Expression
1 mdandyvrx10.2 . 2 (𝜓𝜎)
2 mdandyvrx10.1 . 2 (𝜑𝜁)
3 mdandyvrx10.3 . 2 (𝜒𝜑)
4 mdandyvrx10.4 . 2 (𝜃𝜓)
5 mdandyvrx10.5 . 2 (𝜏𝜑)
6 mdandyvrx10.6 . 2 (𝜂𝜓)
71, 2, 3, 4, 5, 6mdandyvrx5 39802 1 ((((𝜒𝜁) ∧ (𝜃𝜎)) ∧ (𝜏𝜁)) ∧ (𝜂𝜎))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 195   ∧ wa 383   ⊻ wxo 1456 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-an 385  df-xor 1457 This theorem is referenced by: (None)
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