Single-mode operation in a large-mode-area fiber laser is highly desired for power scaling. We have, for the first time, demonstrated a 50μm-core-diameter Yb-doped all-solid photonic bandgap fiber laser with a mode area over 4 times that of the previous demonstration. 75W output power has been generated with a diffraction-limited beam and an efficiency of 70% relative to the launched pump power. We have also experimentally confirmed that a robust single-mode regime exists near the high frequency edge of the bandgap. These fibers only guide light within the bandgap over a narrow spectral range, which is essential for lasing far from the gain peak and suppression of stimulated Raman scattering. This work demonstrates the strong potential for mode area scaling of in single-mode all-solid photonic bandgap fibers.