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Theorem keephyp2v 3717
 Description: Keep a hypothesis containing 2 class variables (for use with the weak deduction theorem dedth 3703). (Contributed by NM, 16-Apr-2005.)
Hypotheses
Ref Expression
keephyp2v.1
keephyp2v.2
keephyp2v.3
keephyp2v.4
keephyp2v.5
keephyp2v.6
Assertion
Ref Expression
keephyp2v

Proof of Theorem keephyp2v
StepHypRef Expression
1 keephyp2v.5 . . 3
2 iftrue 3668 . . . . . 6
32eqcomd 2358 . . . . 5
4 keephyp2v.1 . . . . 5
53, 4syl 15 . . . 4
6 iftrue 3668 . . . . . 6
76eqcomd 2358 . . . . 5
8 keephyp2v.2 . . . . 5
97, 8syl 15 . . . 4
105, 9bitrd 244 . . 3
111, 10mpbii 202 . 2
12 keephyp2v.6 . . 3
13 iffalse 3669 . . . . . 6
1413eqcomd 2358 . . . . 5
15 keephyp2v.3 . . . . 5
1614, 15syl 15 . . . 4
17 iffalse 3669 . . . . . 6
1817eqcomd 2358 . . . . 5
19 keephyp2v.4 . . . . 5
2018, 19syl 15 . . . 4
2116, 20bitrd 244 . . 3
2212, 21mpbii 202 . 2
2311, 22pm2.61i 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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