Theorem cbvrlamh ≪ | index | src | ≫ 

theorem cbvrlamh {x y: nat} (a b c: nat x y):
  $ FN/ y b $ >
  $ FN/ x c $ >
  $ x = y -> b = c $ >
  $ \. x e. a, b = \. y e. a, c $;
StepHypRefExpression
1 lowereq 
(\ x, b) |` a == (\ y, c) |` a -> lower ((\ x, b) |` a) = lower ((\ y, c) |` a)
2 1 conv rlam 
(\ x, b) |` a == (\ y, c) |` a -> \. x e. a, b = \. y e. a, c
3 reseq1 
\ x, b == \ y, c -> (\ x, b) |` a == (\ y, c) |` a
4 hyp h1 
FN/ y b
5 hyp h2 
FN/ x c
6 hyp e 
x = y -> b = c
7 4, 5, 6 cbvlamh 
\ x, b == \ y, c
8 3, 7 ax_mp 
(\ x, b) |` a == (\ y, c) |` a
9 2, 8 ax_mp 
\. x e. a, b = \. y e. a, c

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 (peano2, addeq, muleq)