{"srcs":[{"typ":"Web","fileName":"","url":"https://us.metamath.org/metamath/set.mm","readInstr":"StopBefore","label":"ax-3","resetNestingLevel":true,"allLabels":[]}],"descr":"Prove syl.","varsText":"","disjText":"","stmts":[{"label":"syl.1","typ":"e","isGoal":false,"cont":"|- ( ph -> ps )","jstfText":""},{"label":"syl.2","typ":"e","isGoal":false,"cont":"|- ( ps -> ch )","jstfText":""},{"label":"3","typ":"p","isGoal":false,"cont":"|- ( ( ps -> ch ) -> ( ph -> ( ps -> ch ) ) )","jstfText":": ax-1"},{"label":"4","typ":"p","isGoal":false,"cont":"|- ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) )","jstfText":": ax-2"},{"label":"2","typ":"p","isGoal":false,"cont":"|- ( ph -> ( ps -> ch ) )","jstfText":"syl.2 3 : ax-mp"},{"label":"1","typ":"p","isGoal":false,"cont":"|- ( ( ph -> ps ) -> ( ph -> ch ) )","jstfText":"2 4 : ax-mp"},{"label":"syl","typ":"p","isGoal":true,"cont":"|- ( ph -> ch )","jstfText":"syl.1 1 : ax-mp"}]}