Using the Bρ-defined isochronous mass spectrometry technique, we report the first determination of the ^{23}Si, ^{26}P, ^{27}S, and ^{31}Ar masses and improve the precision of the ^{28}S mass by a factor of 11. Our measurements confirm that these isotopes are bound and fix the location of the proton dripline in P, S, and Ar. We find that the mirror energy differences of the mirror-nuclei pairs ^{26}P-^{26}Na, ^{27}P-^{27}Mg, ^{27}S-^{27}Na, ^{28}S-^{28}Mg, and ^{31}Ar-^{31}Al …