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Theorem exlimd2 1483
 Description: Deduction from Theorem 19.23 of [Margaris] p. 90. Similar to exlimdh 1484 but with one slightly different hypothesis. (Contributed by Jim Kingdon, 30-Dec-2017.)
Hypotheses
Ref Expression
exlimd2.1 (φxφ)
exlimd2.2 (φ → (χxχ))
exlimd2.3 (φ → (ψχ))
Assertion
Ref Expression
exlimd2 (φ → (xψχ))

Proof of Theorem exlimd2
StepHypRef Expression
1 exlimd2.1 . . 3 (φxφ)
2 exlimd2.2 . . 3 (φ → (χxχ))
31, 2alrimih 1355 . 2 (φx(χxχ))
4 exlimd2.3 . . 3 (φ → (ψχ))
51, 4alrimih 1355 . 2 (φx(ψχ))
6 19.23ht 1383 . . 3 (x(χxχ) → (x(ψχ) ↔ (xψχ)))
76biimpd 132 . 2 (x(χxχ) → (x(ψχ) → (xψχ)))
83, 5, 7sylc 56 1 (φ → (xψχ))
 Colors of variables: wff set class Syntax hints:   → wi 4  ∀wal 1240  ∃wex 1378 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-5 1333  ax-gen 1335  ax-ie2 1380 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  equsexd  1614  cbvexdh  1798
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