Theorem sscpl2 | index | src |

theorem sscpl2 (A B: set): $ A C_ Compl B <-> B C_ Compl A $;
StepHypRefExpression
1 bitr3
(A i^i B == 0 <-> A C_ Compl B) -> (A i^i B == 0 <-> B C_ Compl A) -> (A C_ Compl B <-> B C_ Compl A)
2 ineq0
A i^i B == 0 <-> A C_ Compl B
3 1, 2 ax_mp
(A i^i B == 0 <-> B C_ Compl A) -> (A C_ Compl B <-> B C_ Compl A)
4 ineq0r
A i^i B == 0 <-> B C_ Compl A
5 3, 4 ax_mp
A C_ Compl B <-> B C_ Compl A

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp, itru), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12), axs_set (elab, ax_8), axs_the (theid, the0), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)