Theorem eqsubsnabd ≪ | index | src | ≫

theorem eqsubsnabd (G: wff) (a: nat) {x: nat} (p: wff x):
  $ G -> p -> x = a $ >
  $ G -> subsn {x | p} $;

Step	Hyp	Ref	Expression
1		subsnss	{x \| p} C_ {x \| x = a} -> subsn {x \| x = a} -> subsn {x \| p}
2		hyp h	G -> p -> x = a
3	2	ssabd	G -> {x \| p} C_ {x \| x = a}
4		subsnsn2	subsn {x \| x = a}
5	4	a1i	G -> subsn {x \| x = a}
6	1, 3, 5	sylc	G -> subsn {x \| 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)