Theorem rlamss | index | src |

theorem rlamss {x: nat} (a b: nat x): $ \. x e. a, b C_ \ x, b $;
StepHypRefExpression
1 sseq1
\. x e. a, b == (\ x, b) |` a -> (\. x e. a, b C_ \ x, b <-> (\ x, b) |` a C_ \ x, b)
2 rlameqs
\. x e. a, b == (\ x, b) |` a
3 1, 2 ax_mp
\. x e. a, b C_ \ x, b <-> (\ x, b) |` a C_ \ x, b
4 resss
(\ x, b) |` a C_ \ x, b
5 3, 4 mpbir
\. x e. a, b C_ \ x, b

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)