Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax12indi Unicode version

Theorem ax12indi 2274
 Description: Induction step for constructing a substitution instance of ax-c15 2220 without using ax-c15 2220. Implication case. (Contributed by NM, 21-Jan-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ax12indn.1
ax12indi.2
Assertion
Ref Expression
ax12indi

Proof of Theorem ax12indi
StepHypRef Expression
1 ax12indn.1 . . . . . 6
21ax12indn 2273 . . . . 5
32imp 429 . . . 4
4 pm2.21 108 . . . . . 6
54imim2i 14 . . . . 5
65alimi 1633 . . . 4
73, 6syl6 33 . . 3
8 ax12indi.2 . . . . 5
98imp 429 . . . 4
10 ax-1 6 . . . . . 6
1110imim2i 14 . . . . 5
1211alimi 1633 . . . 4
139, 12syl6 33 . . 3
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613