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Theorem exdistrfor 1663
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  F/
Assertion
Ref Expression
exdistrfor

Proof of Theorem exdistrfor
StepHypRef Expression
1 exdistrfor.1 . 2  F/
2 biidd 161 . . . . . 6
32drex1 1661 . . . . 5
43drex2 1602 . . . 4
5 hbe1 1365 . . . . . 6
6519.9h 1516 . . . . 5
7 19.8a 1464 . . . . . . 7
87anim2i 324 . . . . . 6
98eximi 1473 . . . . 5
106, 9sylbi 114 . . . 4
114, 10syl6bir 153 . . 3
12 ax-ial 1409 . . . 4  F/  F/
13 19.40 1504 . . . . . 6
14 19.9t 1515 . . . . . . . 8  F/
1514biimpd 132 . . . . . . 7  F/
1615anim1d 319 . . . . . 6  F/
1713, 16syl5 28 . . . . 5  F/
1817sps 1412 . . . 4  F/
1912, 18eximdh 1484 . . 3  F/
2011, 19jaoi 623 . 2  F/
211, 20ax-mp 7 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wo 616  wal 1226   F/wnf 1329  wex 1362
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409
This theorem depends on definitions:  df-bi 110  df-nf 1330
This theorem is referenced by:  oprabidlem  5460
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