Theorem lteq | index | src |

theorem lteq (_a1 _a2 _b1 _b2: nat):
  $ _a1 = _a2 -> _b1 = _b2 -> (_a1 < _b1 <-> _a2 < _b2) $;
StepHypRefExpression
1 anl
_a1 = _a2 /\ _b1 = _b2 -> _a1 = _a2
2 anr
_a1 = _a2 /\ _b1 = _b2 -> _b1 = _b2
3 1, 2 lteqd
_a1 = _a2 /\ _b1 = _b2 -> (_a1 < _b1 <-> _a2 < _b2)
4 3 exp
_a1 = _a2 -> _b1 = _b2 -> (_a1 < _b1 <-> _a2 < _b2)

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)