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Theorem gencbvex 2901
 Description: Change of bound variable using implicit substitution. (Contributed by NM, 17-May-1996.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Hypotheses
Ref Expression
gencbvex.1
gencbvex.2
gencbvex.3
gencbvex.4
Assertion
Ref Expression
gencbvex
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()   ()

Proof of Theorem gencbvex
StepHypRef Expression
1 excom 1741 . 2
2 gencbvex.1 . . . 4
3 gencbvex.3 . . . . . . 7
4 gencbvex.2 . . . . . . 7
53, 4anbi12d 691 . . . . . 6
65bicomd 192 . . . . 5
76eqcoms 2356 . . . 4
82, 7ceqsexv 2894 . . 3
98exbii 1582 . 2
10 19.41v 1901 . . . 4
11 simpr 447 . . . . 5
12 gencbvex.4 . . . . . . . 8
13 eqcom 2355 . . . . . . . . . . 11
1413biimpi 186 . . . . . . . . . 10
1514adantl 452 . . . . . . . . 9
1615eximi 1576 . . . . . . . 8
1712, 16sylbi 187 . . . . . . 7
1817adantr 451 . . . . . 6
1918ancri 535 . . . . 5
2011, 19impbii 180 . . . 4
2110, 20bitri 240 . . 3
2221exbii 1582 . 2
231, 9, 223bitr3i 266 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wex 1541   wceq 1642   wcel 1710  cvv 2859 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-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861 This theorem is referenced by:  gencbvex2  2902  gencbval  2903
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