theorem ifpneg2 (a b c: wff): $ ~b -> (ifp a b c <-> ~a /\ c) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
ifpnot |
ifp (~a) c b <-> ifp a b c |
| 2 |
|
ifpneg3 |
~b -> (ifp (~a) c b <-> ~a /\ c) |
| 3 |
1, 2 |
syl5bbr |
~b -> (ifp a b c <-> ~a /\ c) |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp)