Theorem funcss3 ≪ | index | src | ≫

theorem funcss3 (A B C F: set): $ B C_ C -> func F A B -> func F A C $;

Step	Hyp	Ref	Expression
1		sstr	Ran F C_ B -> B C_ C -> Ran F C_ C
2	1	com12	B C_ C -> Ran F C_ B -> Ran F C_ C
3	2	anim2d	B C_ C -> isfun F /\ Dom F == A /\ Ran F C_ B -> isfun F /\ Dom F == A /\ Ran F C_ C
4	3	conv func	B C_ C -> func F A B -> func F A C

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_12), axs_set (ax_8)