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Theorem 19.29 1493
 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 1324 . . 3 (xφx(ψ → (φ ψ)))
3 exim 1472 . . 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 1226  ∃wex 1362 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 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-4 1381  ax-ial 1409 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  19.29r  1494  19.29x  1496  19.35-1  1497  equs4  1595  equvini  1623  rexxfrd  4145  funimaexglem  4908  bj-inex  7130
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