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Theorem exdistrfor 1780
 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 Jim Kingdon, 25-Feb-2018.)
Hypothesis
Ref Expression
exdistrfor.1
Assertion
Ref Expression
exdistrfor

Proof of Theorem exdistrfor
StepHypRef Expression
1 exdistrfor.1 . 2
2 biidd 171 . . . . . 6
32drex1 1778 . . . . 5
43drex2 1712 . . . 4
5 hbe1 1475 . . . . . 6
6519.9h 1623 . . . . 5
7 19.8a 1570 . . . . . . 7
87anim2i 340 . . . . . 6
98eximi 1580 . . . . 5
106, 9sylbi 120 . . . 4
114, 10syl6bir 163 . . 3
12 ax-ial 1514 . . . 4
13 19.40 1611 . . . . . 6
14 19.9t 1622 . . . . . . . 8
1514biimpd 143 . . . . . . 7
1615anim1d 334 . . . . . 6
1713, 16syl5 32 . . . . 5
1817sps 1517 . . . 4
1912, 18eximdh 1591 . . 3
2011, 19jaoi 706 . 2
211, 20ax-mp 5 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wo 698  wal 1333  wnf 1440  wex 1472 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514 This theorem depends on definitions:  df-bi 116  df-nf 1441 This theorem is referenced by:  oprabidlem  5849
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