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Theorem exdistrf 2075
 Description: Distribution of existential quantifiers, with a bound-variable hypothesis saying that is not free in , but can be free in (and there is no distinct variable condition on and ). (Contributed by Mario Carneiro, 20-Mar-2013.) (Proof shortened by Wolf Lammen, 14-May-2018.)
Hypothesis
Ref Expression
exdistrf.1
Assertion
Ref Expression
exdistrf

Proof of Theorem exdistrf
StepHypRef Expression
1 nfe1 1840 . 2
2 19.8a 1857 . . . . . 6
32anim2i 569 . . . . 5
43eximi 1656 . . . 4
5 biidd 237 . . . . 5
65drex1 2069 . . . 4
74, 6syl5ibr 221 . . 3
8 19.40 1679 . . . 4
9 exdistrf.1 . . . . . 6
10919.9d 1892 . . . . 5
1110anim1d 564 . . . 4
12 19.8a 1857 . . . 4
138, 11, 12syl56 34 . . 3
147, 13pm2.61i 164 . 2
151, 14exlimi 1912 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612  F/wnf 1616 This theorem is referenced by:  oprabid  6323 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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