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Theorem 19.40-2 1610
Description: Theorem *11.42 in [WhiteheadRussell] p. 163. Theorem 19.40 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
19.40-2 (xy(φ ψ) → (xyφ xyψ))

Proof of Theorem 19.40-2
StepHypRef Expression
1 19.40 1609 . . 3 (y(φ ψ) → (yφ yψ))
21eximi 1576 . 2 (xy(φ ψ) → x(yφ yψ))
3 19.40 1609 . 2 (x(yφ yψ) → (xyφ xyψ))
42, 3syl 15 1 (xy(φ ψ) → (xyφ xyψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358  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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