Theorem eqeq | index | src |

theorem eqeq (a b c d: nat): $ a = b -> c = d -> (a = c <-> b = d) $;
StepHypRefExpression
1 anl
a = b /\ c = d -> a = b
2 anr
a = b /\ c = d -> c = d
3 1, 2 eqeqd
a = b /\ c = d -> (a = c <-> b = d)
4 3 exp
a = b -> c = d -> (a = c <-> b = d)

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)