Theorem ifeq2a ≪ | index | src | ≫ 

theorem ifeq2a (a b c: nat) (p: wff): $ (p -> a = b) -> if p a c = if p b c $;
StepHypRefExpression
1 ifeq2 
a = b -> if p a c = if p b c
2 1 imim2i 
(p -> a = b) -> p -> if p a c = if p b c
3 ifneg 
~p -> if p a c = c
4 ifneg 
~p -> if p b c = c
5 3, 4 eqtr4d 
~p -> if p a c = if p b c
6 5 a1i 
(p -> a = b) -> ~p -> if p a c = if p b c
7 2, 6 casesd 
(p -> a = b) -> if p a c = if p b 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)