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Theorem a9wa9lem3 1407
Description: Lemma for a9wa9 1415. Similar to ax4 1423, without using ax-9 1418 or ax-4 1392.
Hypotheses
Ref Expression
a9wa9lem3.1
a9wa9lem3.2
Assertion
Ref Expression
a9wa9lem3
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem a9wa9lem3
StepHypRef Expression
1 a9wa9lem3.1 . 2
2 ax-17 1402 . . 3
3 a9wa9lem3.2 . . . . . . . 8
43a9wa9lem1 1404 . . . . . . 7
5 ax-17 1402 . . . . . . 7
6 ax-11 1389 . . . . . . 7
74, 5, 6syl2im 33 . . . . . 6
8 con2 551 . . . . . . . 8
98al2imi 1348 . . . . . . 7
103, 9mtoi 569 . . . . . 6
117, 10syl6 28 . . . . 5
1211con4d 715 . . . 4
1312con3i 543 . . 3
142, 13alrimi 1352 . 2
151, 14mt3 724 1
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4  wal 1335
This theorem is referenced by:  a9wa9lem4  1408  a9wa9lem5  1409  a9wa9lem6  1410  a9wa9lem6OLD  1411  a9wa9lem8  1413  a9wa9lem8OLD  1414  a9wa9  1415  a9wa9OLD  1416
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-in1 527  ax-in2 528  ax-5 1336  ax-gen 1339  ax-8 1387  ax-11 1389  ax-17 1402
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