Theorem birexexi | index | src |

theorem birexexi {x y: nat} (a b: wff x y) (q: wff y):
  $ a <-> E. y (q /\ b) $ >
  $ E. x a <-> E. y (q /\ E. x b) $;
StepHypRefExpression
1 bitr4
(E. x a <-> E. x E. y (q /\ b)) -> (E. y (q /\ E. x b) <-> E. x E. y (q /\ b)) -> (E. x a <-> E. y (q /\ E. x b))
2 hyp h
a <-> E. y (q /\ b)
3 2 exeqi
E. x a <-> E. x E. y (q /\ b)
4 1, 3 ax_mp
(E. y (q /\ E. x b) <-> E. x E. y (q /\ b)) -> (E. x a <-> E. y (q /\ E. x b))
5 rexexcomb
E. y (q /\ E. x b) <-> E. x E. y (q /\ b)
6 4, 5 ax_mp
E. x a <-> E. y (q /\ E. x 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)