Theorem dvdeqd | index | src |

theorem dvdeqd (_G: wff) (_a1 _a2 _b1 _b2: nat):
  $ _G -> _a1 = _a2 $ >
  $ _G -> _b1 = _b2 $ >
  $ _G -> (_a1 || _b1 <-> _a2 || _b2) $;
StepHypRefExpression
1 eqidd
_G -> c = c
2 hyp _ah
_G -> _a1 = _a2
3 1, 2 muleqd
_G -> c * _a1 = c * _a2
4 hyp _bh
_G -> _b1 = _b2
5 3, 4 eqeqd
_G -> (c * _a1 = _b1 <-> c * _a2 = _b2)
6 5 exeqd
_G -> (E. c c * _a1 = _b1 <-> E. c c * _a2 = _b2)
7 6 conv dvd
_G -> (_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 (muleq)