let S1, S2 be non empty ManySortedSign ; ( ex f, g being one-to-one Function st S1,S2 are_equivalent_wrt f,g implies ex f, g being one-to-one Function st S2,S1 are_equivalent_wrt f,g )
given f, g being one-to-one Function such that A1:
S1,S2 are_equivalent_wrt f,g
; ex f, g being one-to-one Function st S2,S1 are_equivalent_wrt f,g
take
f "
; ex g being one-to-one Function st S2,S1 are_equivalent_wrt f " ,g
take
g "
; S2,S1 are_equivalent_wrt f " ,g "
thus
S2,S1 are_equivalent_wrt f " ,g "
by A1, Th27; verum