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Theorem a9wa9lem8 1413
Description: Lemma for a9wa9 1415. Similar to dvelimfALT 1585, without using ax-9 1418 or ax-4 1392. (The proof was shortened by Wolf Lammen, 18-Jul-2014.)
Hypotheses
Ref Expression
a9wa9.1
a9wa9.2
a9wa9.3
a9wa9.4
a9wa9.5
a9wa9lem8.6
Assertion
Ref Expression
a9wa9lem8
Distinct variable groups:   ,,   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)

Proof of Theorem a9wa9lem8
StepHypRef Expression
1 ax-17 1402 . . . . . 6
21a1d 21 . . . . . 6
31, 2alrimi 1352 . . . . 5
4 a9wa9.4 . . . . . . . . 9
5 a9wa9.5 . . . . . . . . 9
64, 5a9wa9lem3 1407 . . . . . . . 8
7 a9wa9lem8.6 . . . . . . . 8
86, 7syl5ibr 144 . . . . . . 7
98a2i 11 . . . . . 6
109alimi 1345 . . . . 5
113, 10syl 14 . . . 4
12 ax-6 1337 . . . . . . . 8
13 ax-10 1388 . . . . . . . . 9
1413con3i 543 . . . . . . . 8
1512, 14alrimi 1352 . . . . . . 7
1615nalequcoms 1401 . . . . . 6
17 ax-17 1402 . . . . . 6
184, 5, 16, 17a9wa9lem7 1412 . . . . 5
19 a9wa9.1 . . . . . 6
20 a9wa9.2 . . . . . 6
21 ax-6 1337 . . . . . . 7
22 ax-6 1337 . . . . . . 7
2319, 20, 21, 22a9wa9lem7 1412 . . . . . 6
24 ax-12 1393 . . . . . . 7
2524imp 114 . . . . . 6
26 a17d 1403 . . . . . 6
2719, 20, 23, 25, 26a9wa9lem6 1410 . . . . 5
2818, 27hbald 1373 . . . 4
297biimpd 131 . . . . . . . 8
3029a2i 11 . . . . . . 7
3130alimi 1345 . . . . . 6
32 a9wa9.3 . . . . . . 7
33 con3 550 . . . . . . . 8
3433al2imi 1348 . . . . . . 7
3532, 34mtoi 569 . . . . . 6
36 ax-17 1402 . . . . . . 7
3736con1i 726 . . . . . 6
3831, 35, 373syl 17 . . . . 5
3938alimi 1345 . . . 4
4011, 28, 39syl56 29 . . 3
4140expcom 108 . 2
4219, 20a9wa9lem3 1407 . . . 4
43 ax-11 1389 . . . 4
4442, 1, 43syl2im 33 . . 3
45 pm2.27 34 . . . 4
4645al2imi 1348 . . 3
4744, 46syld 39 . 2
4841, 47pm2.61d2 737 1
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 96   wb 97  wal 1335
This theorem is referenced by:  a9wa9  1415  a9wa9OLD  1416
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-io 607  ax-5 1336  ax-6 1337  ax-7 1338  ax-gen 1339  ax-8 1387  ax-10 1388  ax-11 1389  ax-i12 1391  ax-4 1392  ax-17 1402
This theorem depends on definitions:  df-bi 109
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