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Theorem cbvrexf 2830
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by FL, 27-Apr-2008.) (Revised by Mario Carneiro, 9-Oct-2016.)
Hypotheses
Ref Expression
cbvralf.1
cbvralf.2
cbvralf.3
cbvralf.4
cbvralf.5
Assertion
Ref Expression
cbvrexf

Proof of Theorem cbvrexf
StepHypRef Expression
1 cbvralf.1 . . . 4
2 cbvralf.2 . . . 4
3 cbvralf.3 . . . . 5
43nfn 1793 . . . 4
5 cbvralf.4 . . . . 5
65nfn 1793 . . . 4
7 cbvralf.5 . . . . 5
87notbid 285 . . . 4
91, 2, 4, 6, 8cbvralf 2829 . . 3
109notbii 287 . 2
11 dfrex2 2627 . 2
12 dfrex2 2627 . 2
1310, 11, 123bitr4i 268 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176  wnf 1544   wceq 1642  wnfc 2476  wral 2614  wrex 2615 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  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620 This theorem is referenced by:  cbvrex  2832
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