Database
SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
Mathbox for Jarvin Udandy
mdandyvrx2
Metamath Proof Explorer
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)
Ref
Expression
Hypotheses
mdandyvrx2.1
|- ( ph \/_ ze )
mdandyvrx2.2
|- ( ps \/_ si )
mdandyvrx2.3
|- ( ch <-> ph )
mdandyvrx2.4
|- ( th <-> ps )
mdandyvrx2.5
|- ( ta <-> ph )
mdandyvrx2.6
|- ( et <-> ph )
Assertion
mdandyvrx2
|- ( ( ( ( ch \/_ ze ) /\ ( th \/_ si ) ) /\ ( ta \/_ ze ) ) /\ ( et \/_ ze ) )
Proof
Step
Hyp
Ref
Expression
1
mdandyvrx2.1
|- ( ph \/_ ze )
2
mdandyvrx2.2
|- ( ps \/_ si )
3
mdandyvrx2.3
|- ( ch <-> ph )
4
mdandyvrx2.4
|- ( th <-> ps )
5
mdandyvrx2.5
|- ( ta <-> ph )
6
mdandyvrx2.6
|- ( et <-> ph )
7
1 3
axorbciffatcxorb
|- ( ch \/_ ze )
8
2 4
axorbciffatcxorb
|- ( th \/_ si )
9
7 8
pm3.2i
|- ( ( ch \/_ ze ) /\ ( th \/_ si ) )
10
1 5
axorbciffatcxorb
|- ( ta \/_ ze )
11
9 10
pm3.2i
|- ( ( ( ch \/_ ze ) /\ ( th \/_ si ) ) /\ ( ta \/_ ze ) )
12
1 6
axorbciffatcxorb
|- ( et \/_ ze )
13
11 12
pm3.2i
|- ( ( ( ( ch \/_ ze ) /\ ( th \/_ si ) ) /\ ( ta \/_ ze ) ) /\ ( et \/_ ze ) )