A novel deep learning paradigm for synthesis imaging by radio interferometry in astronomy was recently proposed, dubbed "Residual-to-Residual DNN series for high-Dynamic range imaging" (R2D2). In this work, we start by shedding light on R2D2's algorithmic structure, interpreting it as a learned version of CLEAN with minor cycles substituted with a deep neural network (DNN) whose training is iteration-specific. We then proceed with R2D2's first demonstration on real data, for monochromatic intensity imaging of the radio galaxy Cygnus A from S band observations with the Very Large Array (VLA). We show that the modeling power of R2D2's learning approach enables delivering high-precision imaging, superseding the resolution of CLEAN, and matching the precision of modern optimization and plug-and-play algorithms, respectively uSARA and AIRI. Requiring few major-cycle iterations only, R2D2 provides a much faster reconstruction than uSARA and AIRI, known to be highly iterative, and is at least as fast as CLEAN.