Theorem Ifeq2 ≪ | index | src | ≫ 

theorem Ifeq2 (p: wff) (_A1 _A2 B: set):
  $ _A1 == _A2 -> If p _A1 B == If p _A2 B $;
StepHypRefExpression
1 id 
_A1 == _A2 -> _A1 == _A2
2 1 Ifeq2d 
_A1 == _A2 -> If p _A1 B == If p _A2 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)