A forcing chain starts at a cell with two candidates and plays out both futures. Assume the first digit and follow the implications from link to link; then return and do the same for the second. Wherever the two branches agree — some cell ends up with the same value either way, or some candidate dies in both — that agreement is a fact, because one of the two starting assumptions must be true.
Both values of the pivot r4c4 (blue) force r7c4 to 7 — the 2 pencilled there (red) cannot survive either branch.
Start at r4c4 holding 2-5. Branch one: r4c4=2 removes 2 from r7c4, whose 2-7 collapses to 7. Branch two: r4c4=5 forces r4c7 (5-7) to 7, which strips the 7 from r7c7 (2-7), making it 2 — and that 2 again clears r7c4 down to 7. Both roads end with r7c4=7, so 7 it is, no matter which way the pivot falls.
One transcription slip anywhere in a branch poisons every conclusion after it. Write the links down (r4c4=2 → r7c4≠2 → r7c4=7) rather than holding them in your head — chains fail in memory, not in logic.