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Theorem keephyp3v 3718
 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 3668 . . . . . 6
32eqcomd 2358 . . . . 5
4 keephyp3v.1 . . . . 5
53, 4syl 15 . . . 4
6 iftrue 3668 . . . . . 6
76eqcomd 2358 . . . . 5
8 keephyp3v.2 . . . . 5
97, 8syl 15 . . . 4
10 iftrue 3668 . . . . . 6
1110eqcomd 2358 . . . . 5
12 keephyp3v.3 . . . . 5
1311, 12syl 15 . . . 4
145, 9, 133bitrd 270 . . 3
151, 14mpbii 202 . 2
16 keephyp3v.8 . . 3
17 iffalse 3669 . . . . . 6
1817eqcomd 2358 . . . . 5
19 keephyp3v.4 . . . . 5
2018, 19syl 15 . . . 4
21 iffalse 3669 . . . . . 6
2221eqcomd 2358 . . . . 5
23 keephyp3v.5 . . . . 5
2422, 23syl 15 . . . 4
25 iffalse 3669 . . . . . 6
2625eqcomd 2358 . . . . 5
27 keephyp3v.6 . . . . 5
2826, 27syl 15 . . . 4
2920, 24, 283bitrd 270 . . 3
3016, 29mpbii 202 . 2
3115, 30pm2.61i 156 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176   wceq 1642  cif 3662 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-if 3663 This theorem is referenced by: (None)
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