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  "body": "\n## Summary\n\nNatural deduction is a proof system whose rules mimic the way mathematicians reason.\nEach connective has introduction rules, which say how to prove a formula with it, and elimination rules, which say how to use such a formula.\nAssumptions can be made for a while and then discharged, as in \"suppose $\\varphi$; then ...; hence $\\varphi \\to \\psi$\".\nIt was introduced by Gerhard Gentzen, and independently by Stanisław Jaśkowski, and it is a basic system of [[proof theory|N4EDJNMTEF]].\n\n## Explanations\n\n### L1 human\n\nTo prove \"if $A$ then $B$\", you usually assume $A$ and show $B$.\nNatural deduction turns this habit into a formal rule, called implication introduction.\nLikewise, to prove \"$A$ and $B$\" you prove $A$ and prove $B$, and from \"$A$ and $B$\" you may conclude $A$.\nProofs are drawn as trees, with the assumptions at the leaves and the conclusion at the root.\nCompared with a [[Hilbert system|1MGMQX43B8]], proofs are shorter and closer to ordinary arguments.\n",
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