Theorem ex_alloc_nf ≪ | index | src | ≫

\ex指配(无关)

theorem ex_alloc_nf {x: set} (A: wff x): $ \nf x A $ > $ A \iff \ex x A $;
StepHypRefExpression
1 iff_comp 
(A \imp \ex x A) \imp (\ex x A \imp A) \imp (A \iff \ex x A)
2 ex_intro 
A \imp \ex x A
3 1, 2 ax_mp 
(\ex x A \imp A) \imp (A \iff \ex x A)
4 hyp n 
\nf x A
5 4 ex_elim_nf 
\ex x A \imp A
6 3, 5 ax_mp 
A \iff \ex x A

Axiom use

Logic (ax_mp, ax_1, ax_2, ax_3, ax_gen, ax_4, ax_5, ax_6, ax_7, ax_12)