Theorem sbeq2d ≪ | index | src | ≫

theorem sbeq2d (_G: wff) {x: nat} (a: nat x) (_p1 _p2: wff x):
  $ _G -> (_p1 <-> _p2) $ >
  $ _G -> ([a / x] _p1 <-> [a / x] _p2) $;

Step	Hyp	Ref	Expression
1		eqidd	_G -> a = a
2		hyp _h	_G -> (_p1 <-> _p2)
3	1, 2	sbeqd	_G -> ([a / x] _p1 <-> [a / x] _p2)

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)