help ∀x∀y(R(x,y) -> R(y,x)) :PR
Ay(R(a,y) -> R(y,a)) :AE1
R(a,b) -> R(b,a) :AE2
R(a,b)( ()/())/(R)(a,a) :AS
R(a,b)( :)/(()/())E4
R(b,a) :->E3,5
R(a,a)( :)/(()/())E4
R(a,a)( ()/())/(R)(a,b)( :)/(()/())I6,7
Et(R(b,t)( ()/())/(R)(a,t))( :)/(()/())I
(R(a,b) ∧ R(a,a)) -> ∃t(R(b,t) ∧ R(a,t)) :->I
∀z((R(a,b) ∧ R(a,z)) -> ∃t(R(b,t) ∧ R(z,t))) :AI
∀y∀z((R(a,y) ∧ R(a,z)) -> ∃t(R(y,t) ∧ R(z,t))) :AI
∀x∀y∀z((R(x,y) ∧ R(x,z)) -> ∃t(R(y,t) ∧ R(z,t))) :AI