"The right conditions" = R (but see the comment below, it's problematic to assume this can be represented with one variable)
Matter = M
Life = L
Intelligence = I
Consciousness = C
"x gives rise to y" = A(x, y)
Using -> for material implication, & for logical conjunction:
[ (R -> A(M, L)) & (R -> A(L, I)) & (R -> A(I, C)) ] -> (R -> A(M, C))
This is a true statement if we also assume that A(x, y) & A(y, z) -> A(x, z) for any x and y.
However, there is an issue about R. Are "the right conditions" to evolve life from matter, really the same "right conditions" to evolve consciousness from intelligence? It seems we might more accurately have four separate "right conditions," one condition for evolving life from matter, one for evolving intelligence from life, one for evolving consciousness from intelligence, and one for evolving intelligence from matter. And if we do that, then the statement is no longer necessarily true.
We could, however, interpret "the right conditions" as the combination of all conditions needed to evolve life from matter, intelligence from life, and consciousness from intelligence. Under this interpretation we can use a single R, and the statement is true.