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Theorem ax12-4 29106
 Description: Study of candidate for ax-12 1866. (Contributed by NM, 7-Nov-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax12-4

Proof of Theorem ax12-4
StepHypRef Expression
1 ax9 1889 . . . 4
2 biidd 228 . . . . . 6
32dral1 1905 . . . . 5
43notbid 285 . . . 4
51, 4mpbiri 224 . . 3
65con2i 112 . 2
7 ax9 1889 . . . 4
8 biidd 228 . . . . . . 7
98dral1 1905 . . . . . 6
109notbid 285 . . . . 5
11 equcom 1647 . . . . . . . 8
1211notbii 287 . . . . . . 7
1312albii 1553 . . . . . 6
1413notbii 287 . . . . 5
1510, 14syl6bb 252 . . . 4
167, 15mpbiri 224 . . 3
1716con2i 112 . 2
18 ax12o 1875 . 2
196, 17, 18sylc 56 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1527 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532
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