Theorem nfss | index | src |

theorem nfss {x: nat} (A B: set x): $ FS/ x A $ > $ FS/ x B $ > $ F/ x A C_ B $;
StepHypRefExpression
1 hyp h1
FS/ x A
2 1 nfel2
F/ x y e. A
3 hyp h2
FS/ x B
4 3 nfel2
F/ x y e. B
5 2, 4 nfim
F/ x y e. A -> y e. B
6 5 nfal
F/ x A. y (y e. A -> y e. B)
7 6 conv subset
F/ x A C_ B

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12), axs_set (ax_8)