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Theorem 19.29r2 1598
Description: Variation of Theorem 19.29 of [Margaris] p. 90 with double quantification. (Contributed by NM, 3-Feb-2005.)
Assertion
Ref Expression
19.29r2 ((xyφ xyψ) → xy(φ ψ))

Proof of Theorem 19.29r2
StepHypRef Expression
1 19.29r 1597 . 2 ((xyφ xyψ) → x(yφ yψ))
2 19.29r 1597 . . 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-1 5  ax-2 6  ax-3 7  ax-mp 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:  2eu6  2289
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