Users' Mathboxes Mathbox for Jarvin Udandy < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  mdandyvr11 Structured version   Visualization version   GIF version

Theorem mdandyvr11 39792
Description: Given the equivalences set in the hypotheses, there exist a proof where ch, th, ta, et match ze, si accordingly. (Contributed by Jarvin Udandy, 7-Sep-2016.)
Hypotheses
Ref Expression
mdandyvr11.1 (𝜑𝜁)
mdandyvr11.2 (𝜓𝜎)
mdandyvr11.3 (𝜒𝜓)
mdandyvr11.4 (𝜃𝜓)
mdandyvr11.5 (𝜏𝜑)
mdandyvr11.6 (𝜂𝜓)
Assertion
Ref Expression
mdandyvr11 ((((𝜒𝜎) ∧ (𝜃𝜎)) ∧ (𝜏𝜁)) ∧ (𝜂𝜎))

Proof of Theorem mdandyvr11
StepHypRef Expression
1 mdandyvr11.2 . 2 (𝜓𝜎)
2 mdandyvr11.1 . 2 (𝜑𝜁)
3 mdandyvr11.3 . 2 (𝜒𝜓)
4 mdandyvr11.4 . 2 (𝜃𝜓)
5 mdandyvr11.5 . 2 (𝜏𝜑)
6 mdandyvr11.6 . 2 (𝜂𝜓)
71, 2, 3, 4, 5, 6mdandyvr4 39785 1 ((((𝜒𝜎) ∧ (𝜃𝜎)) ∧ (𝜏𝜁)) ∧ (𝜂𝜎))
Colors of variables: wff setvar class
Syntax hints:  wb 195  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-an 385
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator