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theorem abid {x: nat} (p: wff x): $ x e. {x | p} <-> p $;

Step	Hyp	Ref	Expression
1		bitr	(x e. {x \| p} <-> [x / x] p) -> ([x / x] p <-> p) -> (x e. {x \| p} <-> p)
2		elab2	x e. {x \| p} <-> [x / x] p
3	1, 2	ax_mp	([x / x] p <-> p) -> (x e. {x \| p} <-> p)
4		sbid	[x / x] p <-> p
5	3, 4	ax_mp	x e. {x \| p} <-> p

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)