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Theorem mdandyvrx2 40484
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
mdandyvrx2.1 (𝜑𝜁)
mdandyvrx2.2 (𝜓𝜎)
mdandyvrx2.3 (𝜒𝜑)
mdandyvrx2.4 (𝜃𝜓)
mdandyvrx2.5 (𝜏𝜑)
mdandyvrx2.6 (𝜂𝜑)
Assertion
Ref Expression
mdandyvrx2 ((((𝜒𝜁) ∧ (𝜃𝜎)) ∧ (𝜏𝜁)) ∧ (𝜂𝜁))

Proof of Theorem mdandyvrx2
StepHypRef Expression
1 mdandyvrx2.1 . . . . 5 (𝜑𝜁)
2 mdandyvrx2.3 . . . . 5 (𝜒𝜑)
31, 2axorbciffatcxorb 40406 . . . 4 (𝜒𝜁)
4 mdandyvrx2.2 . . . . 5 (𝜓𝜎)
5 mdandyvrx2.4 . . . . 5 (𝜃𝜓)
64, 5axorbciffatcxorb 40406 . . . 4 (𝜃𝜎)
73, 6pm3.2i 471 . . 3 ((𝜒𝜁) ∧ (𝜃𝜎))
8 mdandyvrx2.5 . . . 4 (𝜏𝜑)
91, 8axorbciffatcxorb 40406 . . 3 (𝜏𝜁)
107, 9pm3.2i 471 . 2 (((𝜒𝜁) ∧ (𝜃𝜎)) ∧ (𝜏𝜁))
11 mdandyvrx2.6 . . 3 (𝜂𝜑)
121, 11axorbciffatcxorb 40406 . 2 (𝜂𝜁)
1310, 12pm3.2i 471 1 ((((𝜒𝜁) ∧ (𝜃𝜎)) ∧ (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:  mdandyvrx13  40495
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