Theorem sbsq | index | src |

theorem sbsq {x: nat} (a: nat) (A: set x): $ x = a -> A == S[a / x] A $;
StepHypRefExpression
1 elsbs
y e. S[a / x] A <-> [a / x] y e. A
2 sbq
x = a -> (y e. A <-> [a / x] y e. A)
3 1, 2 syl6bbr
x = a -> (y e. A <-> y e. S[a / x] A)
4 3 eqrd
x = a -> A == S[a / x] A

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)