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Theorem elimhyp2v 3790
 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 3747 . . . . . 6
21eqcomd 2443 . . . . 5
3 elimhyp2v.1 . . . . 5
42, 3syl 16 . . . 4
5 iftrue 3747 . . . . . 6
65eqcomd 2443 . . . . 5
7 elimhyp2v.2 . . . . 5
86, 7syl 16 . . . 4
94, 8bitrd 246 . . 3
109ibi 234 . 2
11 elimhyp2v.5 . . 3
12 iffalse 3748 . . . . . 6
1312eqcomd 2443 . . . . 5
14 elimhyp2v.3 . . . . 5
1513, 14syl 16 . . . 4
16 iffalse 3748 . . . . . 6
1716eqcomd 2443 . . . . 5
18 elimhyp2v.4 . . . . 5
1917, 18syl 16 . . . 4
2015, 19bitrd 246 . . 3
2111, 20mpbii 204 . 2
2210, 21pm2.61i 159 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wceq 1653  cif 3741 This theorem is referenced by:  omlsi  22908 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-if 3742
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