Theorem bian1exd ≪ | index | src | ≫

theorem bian1exd (G b: wff) {x: nat} (a c: wff x):
  $ G -> (a <-> b /\ c) $ >
  $ G -> (E. x a <-> b /\ E. x c) $;

Step	Hyp	Ref	Expression
1		exan1	E. x (b /\ c) <-> b /\ E. x c
2		hyp h	G -> (a <-> b /\ c)
3	2	exeqd	G -> (E. x a <-> E. x (b /\ c))
4	1, 3	syl6bb	G -> (E. x a <-> b /\ E. x c)

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5)