Theorem splitb1 ≪ | index | src | ≫ 

theorem splitb1 (G: wff) (a b c: nat) (p: wff):
  $ G -> a = b1 c -> p $ >
  $ G -> b = c -> a = b1 b -> p $;
StepHypRefExpression
1 hyp h 
G -> a = b1 c -> p
2 anll 
G /\ b = c /\ a = b1 b -> G
3 anr 
G /\ b = c /\ a = b1 b -> a = b1 b
4 anlr 
G /\ b = c /\ a = b1 b -> b = c
5 4 b1eqd 
G /\ b = c /\ a = b1 b -> b1 b = b1 c
6 3, 5 eqtrd 
G /\ b = c /\ a = b1 b -> a = b1 c
7 1, 2, 6 sylc 
G /\ b = c /\ a = b1 b -> p
8 7 exp 
G /\ b = c -> a = b1 b -> p
9 8 exp 
G -> b = c -> a = b1 b -> p

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), axs_peano (peano2, addeq)