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Theorem elimhyp2v 3711
 Description: Eliminate a hypothesis containing 2 class variables. (Contributed by NM, 14-Aug-1999.)
Hypotheses
Ref Expression
elimhyp2v.1
elimhyp2v.2
elimhyp2v.3
elimhyp2v.4
elimhyp2v.5
Assertion
Ref Expression
elimhyp2v

Proof of Theorem elimhyp2v
StepHypRef Expression
1 iftrue 3668 . . . . . 6
21eqcomd 2358 . . . . 5
3 elimhyp2v.1 . . . . 5
42, 3syl 15 . . . 4
5 iftrue 3668 . . . . . 6
65eqcomd 2358 . . . . 5
7 elimhyp2v.2 . . . . 5
86, 7syl 15 . . . 4
94, 8bitrd 244 . . 3
109ibi 232 . 2
11 elimhyp2v.5 . . 3
12 iffalse 3669 . . . . . 6
1312eqcomd 2358 . . . . 5
14 elimhyp2v.3 . . . . 5
1513, 14syl 15 . . . 4
16 iffalse 3669 . . . . . 6
1716eqcomd 2358 . . . . 5
18 elimhyp2v.4 . . . . 5
1917, 18syl 15 . . . 4
2015, 19bitrd 244 . . 3
2111, 20mpbii 202 . 2
2210, 21pm2.61i 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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