Mathbox for Jarvin Udandy < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  mdandyvrx14 Structured version   Visualization version   GIF version

Theorem mdandyvrx14 39811
 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
mdandyvrx14.1 (𝜑𝜁)
mdandyvrx14.2 (𝜓𝜎)
mdandyvrx14.3 (𝜒𝜑)
mdandyvrx14.4 (𝜃𝜓)
mdandyvrx14.5 (𝜏𝜓)
mdandyvrx14.6 (𝜂𝜓)
Assertion
Ref Expression
mdandyvrx14 ((((𝜒𝜁) ∧ (𝜃𝜎)) ∧ (𝜏𝜎)) ∧ (𝜂𝜎))

Proof of Theorem mdandyvrx14
StepHypRef Expression
1 mdandyvrx14.2 . 2 (𝜓𝜎)
2 mdandyvrx14.1 . 2 (𝜑𝜁)
3 mdandyvrx14.3 . 2 (𝜒𝜑)
4 mdandyvrx14.4 . 2 (𝜃𝜓)
5 mdandyvrx14.5 . 2 (𝜏𝜓)
6 mdandyvrx14.6 . 2 (𝜂𝜓)
71, 2, 3, 4, 5, 6mdandyvrx1 39798 1 ((((𝜒𝜁) ∧ (𝜃𝜎)) ∧ (𝜏𝜎)) ∧ (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)
 Copyright terms: Public domain W3C validator