Theorem sabssi ≪ | index | src | ≫ 

theorem sabssi {x: nat} (A B: set x): $ A C_ B $ > $ S\ x, A C_ S\ x, B $;
StepHypRefExpression
1 sabss 
S\ x, A C_ S\ x, B <-> A. x A C_ B
2 hyp h 
A C_ B
3 2 ax_gen 
A. x A C_ B
4 1, 3 mpbir 
S\ x, A C_ S\ 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)