Theorem bian1exi ≪ | index | src | ≫ 

theorem bian1exi (b: wff) {x: nat} (a c: wff x):
  $ a <-> b /\ c $ >
  $ E. x a <-> b /\ E. x c $;
StepHypRefExpression
1 bitr 
(E. x a <-> E. x (b /\ c)) -> (E. x (b /\ c) <-> b /\ E. x c) -> (E. x a <-> b /\ E. x c)
2 hyp h 
a <-> b /\ c
3 2 exeqi 
E. x a <-> E. x (b /\ c)
4 1, 3 ax_mp 
(E. x (b /\ c) <-> b /\ E. x c) -> (E. x a <-> b /\ E. x c)
5 exan1 
E. x (b /\ c) <-> b /\ E. x c
6 4, 5 ax_mp 
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)