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theorem a3d (a b c: wff): $ a -> ~b -> ~c $ > $ a -> c -> b $;

Step	Hyp	Ref	Expression
1		ax_3	(~b -> ~c) -> c -> b
2		hyp h	a -> ~b -> ~c
3	1, 2	syl	a -> c -> b

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)