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Theorem ax11indi 1814
Description: Induction step for constructing a substitution instance of ax-11o 1654 without using ax-11o 1654. Implication case.
Hypotheses
Ref Expression
ax11indn.1
ax11indi.2
Assertion
Ref Expression
ax11indi

Proof of Theorem ax11indi
StepHypRef Expression
1 ax11indn.1 . . . . . 6
21ax11indn 1813 . . . . 5
32imp 114 . . . 4
4 pm2.21 530 . . . . . 6
54imim2i 12 . . . . 5
65alimi 1345 . . . 4
73, 6syl6 28 . . 3
8 ax11indi.2 . . . . 5
98imp 114 . . . 4
10 ax-1 5 . . . . . 6
1110imim2i 12 . . . . 5
1211alimi 1345 . . . 4
139, 12syl6 28 . . 3
147, 13jad 739 . 2
1514ex 107 1
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 96  wal 1335
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ia1 98  ax-ia2 99  ax-ia3 100  ax-in1 527  ax-in2 528  ax-5 1336  ax-6 1337  ax-gen 1339  ax-ie1 1375  ax-ie2 1376  ax-4 1392  ax-ial 1430
This theorem depends on definitions:  df-bi 109  df-tru 1313  df-fal 1314
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