Theorem eqri2 ≪ | index | src | ≫ 

theorem eqri2 (A B: set) {x y: nat}: $ x, y e. A <-> x, y e. B $ > $ A == B $;
StepHypRefExpression
1 hyp h 
x, y e. A <-> x, y e. B
2 1 a1i 
T. -> (x, y e. A <-> x, y e. B)
3 2 eqrd2 
T. -> A == B
4 3 trud 
A == B

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp, itru), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12), axs_set (elab, ax_8), axs_the (theid, the0), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)