Theorem cbvrlamd ≪ | index | src | ≫ 

theorem cbvrlamd {x y: nat} (G: wff) (a: nat x y) (b: nat x) (c: nat y):
  $ G /\ x = y -> b = c $ >
  $ G -> \. x e. a, b = \. y e. a, c $;
StepHypRefExpression
1 cbvrlams 
\. x e. a, b = \. y e. a, N[y / x] b
2 1 a1i 
G -> \. x e. a, b = \. y e. a, N[y / x] b
3 sbnet 
A. x (x = y -> b = c) -> N[y / x] b = c
4 hyp h 
G /\ x = y -> b = c
5 4 ialda 
G -> A. x (x = y -> b = c)
6 3, 5 syl 
G -> N[y / x] b = c
7 6 rlameq2d 
G -> \. y e. a, N[y / x] b = \. y e. a, c
8 2, 7 eqtrd 
G -> \. 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)