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?

The structure of rational and ruled symplectic 4-manifolds), $M$ is a blow-up of either $\mathbb{C}P^2$ or of a ruled manifold (i.e. the total space of an $S^2$-fibration). You might find an answer to your question in her (and Lalonde's) related works, which focus on spheres and isotopies of symplectic forms on these manifolds. $\endgroup$On Stein ﬁllings of contact torus bundles(Bull. LMS 48, 2016), within the proof of Theorem 3.5. I think that there is an argument using adjunction alone as well. (Both arguments use McDuff's theorem, as mentioned by Chris above.) $\endgroup$2more comments