Theorem eqsubsnd ≪ | index | src | ≫ 

theorem eqsubsnd (A: set) (G: wff) (a: nat) {x: nat}:
  $ G -> x e. A -> x = a $ >
  $ G -> subsn A $;
StepHypRefExpression
1 subsnss 
A C_ {x | x = a} -> subsn {x | x = a} -> subsn A
2 ssab2 
A. x (x e. A -> x = a) <-> A C_ {x | x = a}
3 hyp h 
G -> x e. A -> x = a
4 3 iald 
G -> A. x (x e. A -> x = a)
5 2, 4 sylib 
G -> A C_ {x | x = a}
6 subsnsn2 
subsn {x | x = a}
7 6 a1i 
G -> subsn {x | x = a}
8 1, 5, 7 sylc 
G -> subsn A

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)