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Theorem mdandyvrx1 40483
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
mdandyvrx1.1 (𝜑𝜁)
mdandyvrx1.2 (𝜓𝜎)
mdandyvrx1.3 (𝜒𝜓)
mdandyvrx1.4 (𝜃𝜑)
mdandyvrx1.5 (𝜏𝜑)
mdandyvrx1.6 (𝜂𝜑)
Assertion
Ref Expression
mdandyvrx1 ((((𝜒𝜎) ∧ (𝜃𝜁)) ∧ (𝜏𝜁)) ∧ (𝜂𝜁))

Proof of Theorem mdandyvrx1
StepHypRef Expression
1 mdandyvrx1.2 . . . . 5 (𝜓𝜎)
2 mdandyvrx1.3 . . . . 5 (𝜒𝜓)
31, 2axorbciffatcxorb 40406 . . . 4 (𝜒𝜎)
4 mdandyvrx1.1 . . . . 5 (𝜑𝜁)
5 mdandyvrx1.4 . . . . 5 (𝜃𝜑)
64, 5axorbciffatcxorb 40406 . . . 4 (𝜃𝜁)
73, 6pm3.2i 471 . . 3 ((𝜒𝜎) ∧ (𝜃𝜁))
8 mdandyvrx1.5 . . . 4 (𝜏𝜑)
94, 8axorbciffatcxorb 40406 . . 3 (𝜏𝜁)
107, 9pm3.2i 471 . 2 (((𝜒𝜎) ∧ (𝜃𝜁)) ∧ (𝜏𝜁))
11 mdandyvrx1.6 . . 3 (𝜂𝜑)
124, 11axorbciffatcxorb 40406 . 2 (𝜂𝜁)
1310, 12pm3.2i 471 1 ((((𝜒𝜎) ∧ (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:  mdandyvrx14  40496
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