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Theorem mdandyvrx7 40489
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
mdandyvrx7.1 (𝜑𝜁)
mdandyvrx7.2 (𝜓𝜎)
mdandyvrx7.3 (𝜒𝜓)
mdandyvrx7.4 (𝜃𝜓)
mdandyvrx7.5 (𝜏𝜓)
mdandyvrx7.6 (𝜂𝜑)
Assertion
Ref Expression
mdandyvrx7 ((((𝜒𝜎) ∧ (𝜃𝜎)) ∧ (𝜏𝜎)) ∧ (𝜂𝜁))

Proof of Theorem mdandyvrx7
StepHypRef Expression
1 mdandyvrx7.2 . . . . 5 (𝜓𝜎)
2 mdandyvrx7.3 . . . . 5 (𝜒𝜓)
31, 2axorbciffatcxorb 40406 . . . 4 (𝜒𝜎)
4 mdandyvrx7.4 . . . . 5 (𝜃𝜓)
51, 4axorbciffatcxorb 40406 . . . 4 (𝜃𝜎)
63, 5pm3.2i 471 . . 3 ((𝜒𝜎) ∧ (𝜃𝜎))
7 mdandyvrx7.5 . . . 4 (𝜏𝜓)
81, 7axorbciffatcxorb 40406 . . 3 (𝜏𝜎)
96, 8pm3.2i 471 . 2 (((𝜒𝜎) ∧ (𝜃𝜎)) ∧ (𝜏𝜎))
10 mdandyvrx7.1 . . 3 (𝜑𝜁)
11 mdandyvrx7.6 . . 3 (𝜂𝜑)
1210, 11axorbciffatcxorb 40406 . 2 (𝜂𝜁)
139, 12pm3.2i 471 1 ((((𝜒𝜎) ∧ (𝜃𝜎)) ∧ (𝜏𝜎)) ∧ (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:  mdandyvrx8  40490
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