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Theorem mdandyvrx0 40482
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 40406 . . . 4 (𝜒𝜁)
4 mdandyvrx0.4 . . . . 5 (𝜃𝜑)
51, 4axorbciffatcxorb 40406 . . . 4 (𝜃𝜁)
63, 5pm3.2i 471 . . 3 ((𝜒𝜁) ∧ (𝜃𝜁))
7 mdandyvrx0.5 . . . 4 (𝜏𝜑)
81, 7axorbciffatcxorb 40406 . . 3 (𝜏𝜁)
96, 8pm3.2i 471 . 2 (((𝜒𝜁) ∧ (𝜃𝜁)) ∧ (𝜏𝜁))
10 mdandyvrx0.6 . . 3 (𝜂𝜑)
111, 10axorbciffatcxorb 40406 . 2 (𝜂𝜁)
129, 11pm3.2i 471 1 ((((𝜒𝜁) ∧ (𝜃𝜁)) ∧ (𝜏𝜁)) ∧ (𝜂𝜁))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 384  wxo 1461
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 386  df-xor 1462
This theorem is referenced by:  mdandyvrx15  40497
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