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Theorem 19.29x 1599
Description: Variation of Theorem 19.29 of [Margaris] p. 90 with mixed quantification. (Contributed by NM, 11-Feb-2005.)
Assertion
Ref Expression
19.29x ((xyφ xyψ) → xy(φ ψ))

Proof of Theorem 19.29x
StepHypRef Expression
1 19.29r 1597 . 2 ((xyφ xyψ) → x(yφ yψ))
2 19.29 1596 . . 3 ((yφ yψ) → y(φ ψ))
32eximi 1576 . 2 (x(yφ yψ) → xy(φ ψ))
41, 3syl 15 1 ((xyφ xyψ) → xy(φ ψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358  wal 1540  wex 1541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
This theorem is referenced by: (None)
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