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Theorem exlimd 1466
Description: Deduction from Theorem 19.9 of [Margaris] p. 89. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof rewritten by Jim Kingdon, 18-Jun-2018.)
Hypotheses
Ref Expression
exlimd.1 xφ
exlimd.2 xχ
exlimd.3 (φ → (ψχ))
Assertion
Ref Expression
exlimd (φ → (xψχ))

Proof of Theorem exlimd
StepHypRef Expression
1 exlimd.1 . . 3 xφ
21nfri 1389 . 2 (φxφ)
3 exlimd.2 . . 3 xχ
43nfri 1389 . 2 (χxχ)
5 exlimd.3 . 2 (φ → (ψχ))
62, 4, 5exlimdh 1465 1 (φ → (xψχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1325  wex 1358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-5 1312  ax-gen 1314  ax-ie2 1360  ax-4 1377
This theorem depends on definitions:  df-bi 110  df-nf 1326
This theorem is referenced by:  exlimdd  1730  ceqsalg  2555  copsex2t  3952  alxfr  4139  mosubopt  4328  ovmpt2df  5551  ovi3  5556  bj-exlimmp  7155
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