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Theorem keepel 3719
Description: Keep a membership hypothesis for weak deduction theorem, when special case is provable. (Contributed by NM, 14-Aug-1999.)
Hypotheses
Ref Expression
keepel.1
keepel.2
Assertion
Ref Expression
keepel

Proof of Theorem keepel
StepHypRef Expression
1 eleq1 2413 . 2
2 eleq1 2413 . 2
3 keepel.1 . 2
4 keepel.2 . 2
51, 2, 3, 4keephyp 3716 1
Colors of variables: wff setvar class
Syntax hints:   wcel 1710  cif 3662
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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:  ifex  3720
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