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Theorem cbvalw 1715
 Description: Change bound variable. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 9-Apr-2017.)
Hypotheses
Ref Expression
cbvalw.1
cbvalw.2
cbvalw.3
cbvalw.4
cbvalw.5
Assertion
Ref Expression
cbvalw
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbvalw
StepHypRef Expression
1 cbvalw.1 . . 3
2 cbvalw.2 . . 3
3 cbvalw.5 . . . 4
43biimpd 200 . . 3
51, 2, 4cbvaliw 1686 . 2
6 cbvalw.3 . . 3
7 cbvalw.4 . . 3
83biimprd 216 . . . 4
98equcoms 1694 . . 3
106, 7, 9cbvaliw 1686 . 2
115, 10impbii 182 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178  wal 1550 This theorem is referenced by:  cbvalvw  1716  hbn1fw  1720  hbn1fwOLD  1721 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552
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