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Theorem 19.29 1508
Description: Theorem 19.29 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
19.29 ((xφ xψ) → x(φ ψ))

Proof of Theorem 19.29
StepHypRef Expression
1 pm3.2 126 . . . 4 (φ → (ψ → (φ ψ)))
21alimi 1341 . . 3 (xφx(ψ → (φ ψ)))
3 exim 1487 . . 3 (x(ψ → (φ ψ)) → (xψx(φ ψ)))
42, 3syl 14 . 2 (xφ → (xψx(φ ψ)))
54imp 115 1 ((xφ xψ) → x(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:  19.29r  1509  19.29x  1511  19.35-1  1512  equs4  1610  equvini  1638  rexxfrd  4161  funimaexglem  4925  bj-inex  9292
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