{"srcs":[{"typ":"Web","fileName":"","url":"https://us.metamath.org/metamath/set.mm","readInstr":"StopBefore","label":"2p2e4","resetNestingLevel":true,"allLabels":[]}],"descr":"Prove that 2 + 2 = 4.","varsText":"","disjText":"","stmts":[{"label":"1","typ":"p","isGoal":false,"cont":"|- 1 e. CC","jstfText":": ax-1cn"},{"label":"2","typ":"p","isGoal":false,"cont":"|- 2 e. CC","jstfText":": 2cn"},{"label":"3","typ":"p","isGoal":false,"cont":"|- 2 = ( 1 + 1 )","jstfText":": df-2"},{"label":"4","typ":"p","isGoal":false,"cont":"|- ( 2 + 2 ) = ( 2 + ( 1 + 1 ) )","jstfText":"3 : oveq2i"},{"label":"5","typ":"p","isGoal":false,"cont":"|- 3 = ( 2 + 1 )","jstfText":": df-3"},{"label":"6","typ":"p","isGoal":false,"cont":"|- 4 = ( 3 + 1 )","jstfText":": df-4"},{"label":"7","typ":"p","isGoal":false,"cont":"|- ( 3 + 1 ) = ( ( 2 + 1 ) + 1 )","jstfText":"5 : oveq1i"},{"label":"8","typ":"p","isGoal":false,"cont":"|- 4 = ( ( 2 + 1 ) + 1 )","jstfText":"6 7 : eqtri"},{"label":"9","typ":"p","isGoal":false,"cont":"|- ( ( 2 + 1 ) + 1 ) = ( 2 + ( 1 + 1 ) )","jstfText":"2 1 1 : addassi"},{"label":"2p2e4","typ":"p","isGoal":true,"cont":"|- ( 2 + 2 ) = 4","jstfText":"9 8 4 : 3eqtr4ri"}]}