Theorem leaddd ≪ | index | src | ≫

theorem leaddd (G: wff) (a b c d: nat):
  $ G -> a <= b $ >
  $ G -> c <= d $ >
  $ G -> a + c <= b + d $;

Step	Hyp	Ref	Expression
1		leadd1	a <= b <-> a + c <= b + c
2		hyp h1	G -> a <= b
3	1, 2	sylib	G -> a + c <= b + c
4		leadd2	c <= d <-> b + c <= b + d
5		hyp h2	G -> c <= d
6	4, 5	sylib	G -> b + c <= b + d
7	3, 6	letrd	G -> a + c <= b + d

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_peano (peano2, peano5, addeq, add0, addS)