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Theorem 19.29x 1511
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 1509 . 2 ((xyφ xyψ) → x(yφ yψ))
2 19.29 1508 . . 3 ((yφ yψ) → y(φ ψ))
32eximi 1488 . 2 (x(yφ yψ) → xy(φ ψ))
41, 3syl 14 1 ((xyφ xyψ) → xy(φ ψ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wal 1240  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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