Theorem resfin ≪ | index | src | ≫ 

theorem resfin (A F: set): $ finite F -> finite (F |` A) $;
StepHypRefExpression
1 finss 
F |` A C_ F -> finite F -> finite (F |` A)
2 resss 
F |` A C_ F
3 1, 2 ax_mp 
finite F -> finite (F |` 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)