Theorem exan1 | index | src |

theorem exan1 {x: nat} (a: wff) (b: wff x): $ E. x (a /\ b) <-> a /\ E. x b $;
StepHypRefExpression
1 anl
a /\ b -> a
2 1 eex
E. x (a /\ b) -> a
3 anr
a /\ b -> b
4 3 eximi
E. x (a /\ b) -> E. x b
5 2, 4 iand
E. x (a /\ b) -> a /\ E. x b
6 ian
a -> b -> a /\ b
7 6 eximd
a -> E. x b -> E. x (a /\ b)
8 7 imp
a /\ E. x b -> E. x (a /\ b)
9 5, 8 ibii
E. x (a /\ b) <-> a /\ 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)