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Theorem keephyp3v 3972
 Description: Keep a hypothesis containing 3 class variables. (Contributed by NM, 27-Sep-1999.)
Hypotheses
Ref Expression
keephyp3v.1
keephyp3v.2
keephyp3v.3
keephyp3v.4
keephyp3v.5
keephyp3v.6
keephyp3v.7
keephyp3v.8
Assertion
Ref Expression
keephyp3v

Proof of Theorem keephyp3v
StepHypRef Expression
1 keephyp3v.7 . . 3
2 iftrue 3912 . . . . . 6
32eqcomd 2428 . . . . 5
4 keephyp3v.1 . . . . 5
53, 4syl 17 . . . 4
6 iftrue 3912 . . . . . 6
76eqcomd 2428 . . . . 5
8 keephyp3v.2 . . . . 5
97, 8syl 17 . . . 4
10 iftrue 3912 . . . . . 6
1110eqcomd 2428 . . . . 5
12 keephyp3v.3 . . . . 5
1311, 12syl 17 . . . 4
145, 9, 133bitrd 282 . . 3
151, 14mpbii 214 . 2
16 keephyp3v.8 . . 3
17 iffalse 3915 . . . . . 6
1817eqcomd 2428 . . . . 5
19 keephyp3v.4 . . . . 5
2018, 19syl 17 . . . 4
21 iffalse 3915 . . . . . 6
2221eqcomd 2428 . . . . 5
23 keephyp3v.5 . . . . 5
2422, 23syl 17 . . . 4
25 iffalse 3915 . . . . . 6
2625eqcomd 2428 . . . . 5
27 keephyp3v.6 . . . . 5
2826, 27syl 17 . . . 4
2920, 24, 283bitrd 282 . . 3
3016, 29mpbii 214 . 2
3115, 30pm2.61i 167 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 187   wceq 1437  cif 3906 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-if 3907 This theorem is referenced by:  sseliALT  4549
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