Theorem sabeqi ≪ | index | src | ≫ 

theorem sabeqi {x: nat} (A B: set x): $ A == B $ > $ S\ x, A == S\ x, B $;
StepHypRefExpression
1 sabeq 
A. x A == B -> S\ x, A == S\ x, B
2 hyp h 
A == B
3 2 ax_gen 
A. x A == B
4 1, 3 ax_mp 
S\ x, A == S\ x, 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)