Theorem imaeq ≪ | index | src | ≫

theorem imaeq (_F1 _F2 _A1 _A2: set):
  $ _F1 == _F2 -> _A1 == _A2 -> _F1 '' _A1 == _F2 '' _A2 $;

Step	Hyp	Ref	Expression
1		anl	_F1 == _F2 /\ _A1 == _A2 -> _F1 == _F2
2		anr	_F1 == _F2 /\ _A1 == _A2 -> _A1 == _A2
3	1, 2	imaeqd	_F1 == _F2 /\ _A1 == _A2 -> _F1 '' _A1 == _F2 '' _A2
4	3	exp	_F1 == _F2 -> _A1 == _A2 -> _F1 '' _A1 == _F2 '' _A2

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)