Theorem ssabd ≪ | index | src | ≫

theorem ssabd (G: wff) {x: nat} (p q: wff x):
  $ G -> p -> q $ >
  $ G -> {x | p} C_ {x | q} $;

Step	Hyp	Ref	Expression
1		ssab	A. x (p -> q) <-> {x \| p} C_ {x \| q}
2		hyp h	G -> p -> q
3	2	iald	G -> A. x (p -> q)
4	1, 3	sylib	G -> {x \| p} C_ {x \| q}

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)