Mathbox for Jarvin Udandy < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  mdandyvrx0 Structured version   Visualization version   GIF version

Theorem mdandyvrx0 43567
 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
mdandyvrx0.1 (𝜑𝜁)
mdandyvrx0.2 (𝜓𝜎)
mdandyvrx0.3 (𝜒𝜑)
mdandyvrx0.4 (𝜃𝜑)
mdandyvrx0.5 (𝜏𝜑)
mdandyvrx0.6 (𝜂𝜑)
Assertion
Ref Expression
mdandyvrx0 ((((𝜒𝜁) ∧ (𝜃𝜁)) ∧ (𝜏𝜁)) ∧ (𝜂𝜁))

Proof of Theorem mdandyvrx0
StepHypRef Expression
1 mdandyvrx0.1 . . . . 5 (𝜑𝜁)
2 mdandyvrx0.3 . . . . 5 (𝜒𝜑)
31, 2axorbciffatcxorb 43491 . . . 4 (𝜒𝜁)
4 mdandyvrx0.4 . . . . 5 (𝜃𝜑)
51, 4axorbciffatcxorb 43491 . . . 4 (𝜃𝜁)
63, 5pm3.2i 474 . . 3 ((𝜒𝜁) ∧ (𝜃𝜁))
7 mdandyvrx0.5 . . . 4 (𝜏𝜑)
81, 7axorbciffatcxorb 43491 . . 3 (𝜏𝜁)
96, 8pm3.2i 474 . 2 (((𝜒𝜁) ∧ (𝜃𝜁)) ∧ (𝜏𝜁))
10 mdandyvrx0.6 . . 3 (𝜂𝜑)
111, 10axorbciffatcxorb 43491 . 2 (𝜂𝜁)
129, 11pm3.2i 474 1 ((((𝜒𝜁) ∧ (𝜃𝜁)) ∧ (𝜏𝜁)) ∧ (𝜂𝜁))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209   ∧ wa 399   ⊻ wxo 1502 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 210  df-an 400  df-xor 1503 This theorem is referenced by:  mdandyvrx15  43582
 Copyright terms: Public domain W3C validator