Theorem cbvpim | index | src |

theorem cbvpim {x y: nat} (p1 q1: wff x) (p2 q2: wff y):
  $ x = y -> (p1 <-> p2) $ >
  $ x = y -> (q1 <-> q2) $ >
  $ (P. x p1 -> q1) <-> (P. y p2 -> q2) $;
StepHypRefExpression
1 nfv
F/ y p1
2 nfv
F/ y q1
3 nfv
F/ x p2
4 nfv
F/ x q2
5 hyp e1
x = y -> (p1 <-> p2)
6 hyp e2
x = y -> (q1 <-> q2)
7 1, 2, 3, 4, 5, 6 cbvpimh
(P. x p1 -> q1) <-> (P. y p2 -> q2)

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, ax_10, ax_11, ax_12)