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Theorem exdistrf 2136
 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 1894 . 2
2 19.8a 1912 . . . . . 6
32anim2i 571 . . . . 5
43eximi 1701 . . . 4
5 biidd 240 . . . . 5
65drex1 2130 . . . 4
74, 6syl5ibr 224 . . 3
8 19.40 1725 . . . 4
9 exdistrf.1 . . . . . 6
10919.9d 1945 . . . . 5
1110anim1d 566 . . . 4
12 19.8a 1912 . . . 4
138, 11, 12syl56 35 . . 3
147, 13pm2.61i 167 . 2
151, 14exlimi 1972 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 370  wal 1435  wex 1657  wnf 1661 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909  ax-13 2058 This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-nf 1662 This theorem is referenced by:  oprabid  6271
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