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Theorem r19.29 2444
Description: Theorem 19.29 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 31-Aug-1999.) (Proof shortened by Andrew Salmon, 30-May-2011.)
Assertion
Ref Expression
r19.29 ((x A φ x A ψ) → x A (φ ψ))

Proof of Theorem r19.29
StepHypRef Expression
1 pm3.2 126 . . . 4 (φ → (ψ → (φ ψ)))
21ralimi 2378 . . 3 (x A φx A (ψ → (φ ψ)))
3 rexim 2407 . . 3 (x A (ψ → (φ ψ)) → (x A ψx A (φ ψ)))
42, 3syl 14 . 2 (x A φ → (x A ψx A (φ ψ)))
54imp 115 1 ((x A φ x A ψ) → x A (φ ψ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wral 2300  wrex 2301
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  df-ral 2305  df-rex 2306
This theorem is referenced by:  r19.29r  2445  r19.29d2r  2449  r19.35-1  2454  triun  3858  ralxfrd  4160  elrnmptg  4529  fun11iun  5090  fmpt  5262  fliftfun  5379  bj-findis  9409
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