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Theorem ax9lem10 29149
 Description: Lemma for ax9 1889. Similar to hban 1736, without using sp 1716, ax9 1889, or ax10 1884. (Contributed by NM, 7-Aug-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ax9lem10.a
ax9lem10.c
ax9lem10.1
ax9lem10.2
Assertion
Ref Expression
ax9lem10
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem ax9lem10
StepHypRef Expression
1 df-an 360 . 2
2 ax9lem10.a . . 3
3 ax9lem10.c . . 3
4 ax9lem10.1 . . . . . 6
52, 3, 4ax9lem8 29147 . . . . 5
6 pm2.21 100 . . . . 5
75, 6alrimih 1552 . . . 4
8 ax9lem10.2 . . . . . 6
92, 3, 8ax9lem8 29147 . . . . 5
10 ax-1 5 . . . . 5
119, 10alrimih 1552 . . . 4
127, 11ja 153 . . 3
132, 3, 12ax9lem8 29147 . 2
141, 13hbxfrbi 1555 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 358  wal 1527 This theorem is referenced by:  ax9lem17  29156 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-8 1643  ax-6 1703  ax-11 1715 This theorem depends on definitions:  df-bi 177  df-an 360
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