Theorem biexrexa | index | src |

theorem biexrexa {x y: nat} (p: wff x) (a b: wff x y):
  $ p -> (a <-> E. y b) $ >
  $ E. x (p /\ a) <-> E. y E. x (p /\ b) $;
StepHypRefExpression
2
hyp h
p -> (a <-> E. y b)
3
E. x (p /\ a) <-> E. x (p /\ E. y b)
5
E. x (p /\ E. y b) <-> E. y E. x (p /\ b)
6
3, 5
E. x (p /\ a) <-> E. y E. x (p /\ b)

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5, ax_11)