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Theorem ax11indi 2246
 Description: Induction step for constructing a substitution instance of ax-11o 2191 without using ax-11o 2191. Implication case. (Contributed by NM, 21-Jan-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ax11indn.1
ax11indi.2
Assertion
Ref Expression
ax11indi

Proof of Theorem ax11indi
StepHypRef Expression
1 ax11indn.1 . . . . . 6
21ax11indn 2245 . . . . 5
32imp 419 . . . 4
4 pm2.21 102 . . . . . 6
54imim2i 14 . . . . 5
65alimi 1565 . . . 4
73, 6syl6 31 . . 3
8 ax11indi.2 . . . . 5
98imp 419 . . . 4
10 ax-1 5 . . . . . 6
1110imim2i 14 . . . . 5
1211alimi 1565 . . . 4
139, 12syl6 31 . . 3
147, 13jad 156 . 2
1514ex 424 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1546 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-11 1757 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548
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