Theorem bian2exd ≪ | index | src | ≫

theorem bian2exd (G c: wff) {x: nat} (a b: wff x):
  $ G -> (a <-> b /\ c) $ >
  $ G -> (E. x a <-> E. x b /\ c) $;

Step	Hyp	Ref	Expression
1		exan2	E. x (b /\ c) <-> E. x b /\ 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 <-> E. x b /\ c)

Axiom use

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