TITLE: Two embedded symplectic spheres with zero square in a symplectic $4$-manifold
QUESTION [7 upvotes]: I am aware that the following result is a classical one (by now). But I am not able to understand who proved it. What should be a proper reference to this statement?
Theorem. Let $M^4$ be a compact symplectic manifold with $\pi_1\ne 0$ and let $S_1$ and $S_2$ be two symplectic spheres embedded in it with $S_1^2=S_2^2=0$. Then $S_1$ and $S_2$ are symplectically isotopic in $M^4$. 
In other words, is there an article/book (say pre 2000) claiming that any two symplectic spheres with zero self-intersection in an irrational ruled (non-minimal) surface are symplectically isotopic?

REPLY [2 votes]: It looks indeed that this question is not as classical is it sounds, so let me provide a  2010 reference to a more general statement, at least to show that there is a reference. This is Proposition 3.2 in the following paper:
https://arxiv.org/abs/1012.4146