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Theorem mdandyvrx3 43368
 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
mdandyvrx3.1 (𝜑𝜁)
mdandyvrx3.2 (𝜓𝜎)
mdandyvrx3.3 (𝜒𝜓)
mdandyvrx3.4 (𝜃𝜓)
mdandyvrx3.5 (𝜏𝜑)
mdandyvrx3.6 (𝜂𝜑)
Assertion
Ref Expression
mdandyvrx3 ((((𝜒𝜎) ∧ (𝜃𝜎)) ∧ (𝜏𝜁)) ∧ (𝜂𝜁))

Proof of Theorem mdandyvrx3
StepHypRef Expression
1 mdandyvrx3.2 . . . . 5 (𝜓𝜎)
2 mdandyvrx3.3 . . . . 5 (𝜒𝜓)
31, 2axorbciffatcxorb 43289 . . . 4 (𝜒𝜎)
4 mdandyvrx3.4 . . . . 5 (𝜃𝜓)
51, 4axorbciffatcxorb 43289 . . . 4 (𝜃𝜎)
63, 5pm3.2i 474 . . 3 ((𝜒𝜎) ∧ (𝜃𝜎))
7 mdandyvrx3.1 . . . 4 (𝜑𝜁)
8 mdandyvrx3.5 . . . 4 (𝜏𝜑)
97, 8axorbciffatcxorb 43289 . . 3 (𝜏𝜁)
106, 9pm3.2i 474 . 2 (((𝜒𝜎) ∧ (𝜃𝜎)) ∧ (𝜏𝜁))
11 mdandyvrx3.6 . . 3 (𝜂𝜑)
127, 11axorbciffatcxorb 43289 . 2 (𝜂𝜁)
1310, 12pm3.2i 474 1 ((((𝜒𝜎) ∧ (𝜃𝜎)) ∧ (𝜏𝜁)) ∧ (𝜂𝜁))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209   ∧ wa 399   ⊻ wxo 1502 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 210  df-an 400  df-xor 1503 This theorem is referenced by:  mdandyvrx12  43377
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