Users' Mathboxes Mathbox for Jarvin Udandy < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  mdandyvrx15 Structured version   Visualization version   GIF version

Theorem mdandyvrx15 41683
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
mdandyvrx15.1 (𝜑𝜁)
mdandyvrx15.2 (𝜓𝜎)
mdandyvrx15.3 (𝜒𝜓)
mdandyvrx15.4 (𝜃𝜓)
mdandyvrx15.5 (𝜏𝜓)
mdandyvrx15.6 (𝜂𝜓)
Assertion
Ref Expression
mdandyvrx15 ((((𝜒𝜎) ∧ (𝜃𝜎)) ∧ (𝜏𝜎)) ∧ (𝜂𝜎))

Proof of Theorem mdandyvrx15
StepHypRef Expression
1 mdandyvrx15.2 . 2 (𝜓𝜎)
2 mdandyvrx15.1 . 2 (𝜑𝜁)
3 mdandyvrx15.3 . 2 (𝜒𝜓)
4 mdandyvrx15.4 . 2 (𝜃𝜓)
5 mdandyvrx15.5 . 2 (𝜏𝜓)
6 mdandyvrx15.6 . 2 (𝜂𝜓)
71, 2, 3, 4, 5, 6mdandyvrx0 41668 1 ((((𝜒𝜎) ∧ (𝜃𝜎)) ∧ (𝜏𝜎)) ∧ (𝜂𝜎))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 382  wxo 1612
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-an 383  df-xor 1613
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator