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Theorem mdandyvrx4 41473
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
mdandyvrx4.1 (𝜑𝜁)
mdandyvrx4.2 (𝜓𝜎)
mdandyvrx4.3 (𝜒𝜑)
mdandyvrx4.4 (𝜃𝜑)
mdandyvrx4.5 (𝜏𝜓)
mdandyvrx4.6 (𝜂𝜑)
Assertion
Ref Expression
mdandyvrx4 ((((𝜒𝜁) ∧ (𝜃𝜁)) ∧ (𝜏𝜎)) ∧ (𝜂𝜁))

Proof of Theorem mdandyvrx4
StepHypRef Expression
1 mdandyvrx4.1 . . . . 5 (𝜑𝜁)
2 mdandyvrx4.3 . . . . 5 (𝜒𝜑)
31, 2axorbciffatcxorb 41393 . . . 4 (𝜒𝜁)
4 mdandyvrx4.4 . . . . 5 (𝜃𝜑)
51, 4axorbciffatcxorb 41393 . . . 4 (𝜃𝜁)
63, 5pm3.2i 470 . . 3 ((𝜒𝜁) ∧ (𝜃𝜁))
7 mdandyvrx4.2 . . . 4 (𝜓𝜎)
8 mdandyvrx4.5 . . . 4 (𝜏𝜓)
97, 8axorbciffatcxorb 41393 . . 3 (𝜏𝜎)
106, 9pm3.2i 470 . 2 (((𝜒𝜁) ∧ (𝜃𝜁)) ∧ (𝜏𝜎))
11 mdandyvrx4.6 . . 3 (𝜂𝜑)
121, 11axorbciffatcxorb 41393 . 2 (𝜂𝜁)
1310, 12pm3.2i 470 1 ((((𝜒𝜁) ∧ (𝜃𝜁)) ∧ (𝜏𝜎)) ∧ (𝜂𝜁))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 383  wxo 1504
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 385  df-xor 1505
This theorem is referenced by:  mdandyvrx11  41480
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