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

Step	Hyp	Ref	Expression
1		ax12indn.1	. . . . . 6
2	1	ax12indn 2273	. . . . 5
3	2	imp 429	. . . 4
4		pm2.21 108	. . . . . 6
5	4	imim2i 14	. . . . 5
6	5	alimi 1633	. . . 4
7	3, 6	syl6 33	. . 3
8		ax12indi.2	. . . . 5
9	8	imp 429	. . . 4
10		ax-1 6	. . . . . 6
11	10	imim2i 14	. . . . 5
12	11	alimi 1633	. . . 4
13	9, 12	syl6 33	. . 3
14	7, 13	jad 162	. 2
15	14	ex 434	1

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