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Theorem exdistrf 2066
 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 1747 . 2
2 19.8a 1762 . . . . . 6
32anim2i 553 . . . . 5
43eximi 1585 . . . 4
5 biidd 229 . . . . 5
65drex1 2059 . . . 4
74, 6syl5ibr 213 . . 3
8 19.40 1619 . . . 4
9 exdistrf.1 . . . . . 6
10919.9d 1796 . . . . 5
1110anim1d 548 . . . 4
12 19.8a 1762 . . . 4
138, 11, 12syl56 32 . . 3
147, 13pm2.61i 158 . 2
151, 14exlimi 1821 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1549  wex 1550  wnf 1553 This theorem is referenced by:  oprabid  6105 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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