let S1, S2 be Element of QC-Sub-WFF ; :: thesis: ( S1 `2 = S2 `2 & CQC_Sub S1 is Element of CQC-WFF & CQC_Sub S2 is Element of CQC-WFF implies CQC_Sub (Sub_& (S1,S2)) is Element of CQC-WFF )
assume A1: ( S1 `2 = S2 `2 & CQC_Sub S1 is Element of CQC-WFF & CQC_Sub S2 is Element of CQC-WFF ) ; :: thesis: CQC_Sub (Sub_& (S1,S2)) is Element of CQC-WFF
( S1 `2 = S2 `2 implies CQC_Sub (Sub_& (S1,S2)) = (CQC_Sub S1) '&' (CQC_Sub S2) ) by Th31;
hence CQC_Sub (Sub_& (S1,S2)) is Element of CQC-WFF by A1, CQC_LANG:9; :: thesis: verum