Theorem sbed | index | src |

theorem sbed (G: wff) {x: nat} (a: nat) (b: wff x) (c: wff):
  $ G /\ x = a -> (b <-> c) $ >
  $ G -> ([a / x] b <-> c) $;
StepHypRefExpression
1 sbet
A. x (x = a -> (b <-> c)) -> ([a / x] b <-> c)
2 hyp e
G /\ x = a -> (b <-> c)
3 2 ialda
G -> A. x (x = a -> (b <-> c))
4 1, 3 syl
G -> ([a / x] b <-> c)

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)