New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  exdistrf Unicode version

Theorem exdistrf 1971
 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 1967 . . . 4
32drex2 1968 . . 3
4 nfe1 1732 . . . . 5
5419.9 1783 . . . 4
6 19.8a 1756 . . . . . 6
76anim2i 552 . . . . 5
87eximi 1576 . . . 4
95, 8sylbi 187 . . 3
103, 9syl6bir 220 . 2
11 nfnae 1956 . . 3
12 19.40 1609 . . . 4
13 exdistrf.1 . . . . . 6
141319.9d 1782 . . . . 5
1514anim1d 547 . . . 4
1612, 15syl5 28 . . 3
1711, 16eximd 1770 . 2
1810, 17pm2.61i 156 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 358  wal 1540  wex 1541  wnf 1544 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  oprabid  5550
 Copyright terms: Public domain W3C validator