Natural Deduction
p + (q + r) <=> (p + q) + r
assume p + (q + r). assume p. p + q. p + q + r. therefore p => p + q + r. assume q + r. assume q. p + q. p + q + r. therefore q => p + q + r. assume r. p + q + r. therefore r => p + q + r. p + q + r. therefore q + r => p + q + r. p + q + r. therefore p + (q + r) => p + q + r. assume p + q + r. assume p + q. assume p. p + (q + r). therefore p => p + (q + r). assume q. q + r. p + (q + r). therefore q => p + (q + r). p + (q + r). therefore p + q => p + (q + r). assume r. q + r. p + (q + r). therefore r => p + (q + r). p + (q + r). therefore p + q + r => p + (q + r). p + (q + r) <=> p + q + r.
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Last Modified : 27-Feb-2023