Theorem sbthd ≪ | index | src | ≫

theorem sbthd (G: wff) (a: nat) {x: nat} (p: wff x):
  $ G /\ x = a -> p $ >
  $ G -> [a / x] p $;

Step	Hyp	Ref	Expression
1		itru	T.
2		bith	p -> T. -> (p <-> T.)
3	1, 2	mpi	p -> (p <-> T.)
4		hyp h	G /\ x = a -> p
5	3, 4	syl	G /\ x = a -> (p <-> T.)
6	5	sbed	G -> ([a / x] p <-> T.)
7	1, 6	mpbiri	G -> [a / 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)