Theorem splitpr ≪ | index | src | ≫

theorem splitpr (G: wff) (a: nat) (p: wff) {x y: nat}:
  $ G -> a = x, y -> p $ >
  $ G -> p $;

Step	Hyp	Ref	Expression
1		expr	E. x E. y a = x, y
2		hyp h	G -> a = x, y -> p
3	2	eexd	G -> E. y a = x, y -> p
4	3	eexd	G -> E. x E. y a = x, y -> p
5	1, 4	mpi	G -> 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), axs_the (theid, the0), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)