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Theorem hbov 111
 Description: Hypothesis builder for binary operation. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypotheses
Ref Expression
hbov.1
hbov.2
hbov.3
hbov.4
hbov.5
hbov.6
hbov.7
Assertion
Ref Expression
hbov

Proof of Theorem hbov
StepHypRef Expression
1 hbov.5 . . . 4
21ax-cb1 29 . . 3
32trud 27 . 2
4 hbov.1 . . . 4
5 hbov.2 . . . 4
6 hbov.4 . . . 4
74, 5, 6wov 72 . . 3
8 hbov.3 . . 3
9 weq 41 . . . 4
104, 5wc 50 . . . . 5
1110, 6wc 50 . . . 4
124, 5, 6df-ov 73 . . . 4
139, 7, 11, 12dfov2 75 . . 3
14 hbov.6 . . . . . 6
154, 5, 8, 1, 14hbc 110 . . . . 5
16 hbov.7 . . . . 5
1710, 6, 8, 15, 16hbc 110 . . . 4
18 wtru 43 . . . 4
1917, 18adantr 55 . . 3
207, 8, 13, 19hbxfrf 107 . 2
213, 20mpdan 35 1
 Colors of variables: type var term Syntax hints:   ht 2  kc 5  kl 6   ke 7  kt 8  kbr 9   wffMMJ2 11  wffMMJ2t 12 This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-simpl 20  ax-simpr 21  ax-id 24  ax-trud 26  ax-cb1 29  ax-cb2 30  ax-wctl 31  ax-wctr 32  ax-weq 40  ax-refl 42  ax-eqmp 45  ax-wc 49  ax-ceq 51  ax-wl 65  ax-distrc 68  ax-leq 69  ax-wov 71  ax-eqtypi 77  ax-eqtypri 80 This theorem depends on definitions:  df-ov 73 This theorem is referenced by:  clf  115  hbct  155  exlimdv  167  cbvf  179  leqf  181  exlimd  183  exmid  199  axrep  220
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