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