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Theorem exdistrf 1924
 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.)
Hypothesis
Ref Expression
exdistrf.1
Assertion
Ref Expression
exdistrf

Proof of Theorem exdistrf
StepHypRef Expression
1 biidd 228 . . . . 5
21drex1 1920 . . . 4
32drex2 1921 . . 3
4 nfe1 1718 . . . . 5
5419.9 1795 . . . 4
6 19.8a 1730 . . . . . 6
76anim2i 552 . . . . 5
87eximi 1566 . . . 4
95, 8sylbi 187 . . 3
103, 9syl6bir 220 . 2
11 nfnae 1909 . . 3
12 19.40 1599 . . . 4
13 exdistrf.1 . . . . . 6
141319.9d 1796 . . . . 5
1514anim1d 547 . . . 4
1612, 15syl5 28 . . 3
1711, 16eximd 1762 . 2
1810, 17pm2.61i 156 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 358  wal 1530  wex 1531  wnf 1534 This theorem is referenced by:  oprabid  5898 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535
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