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Theorem cbv2 1981
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.)
Hypotheses
Ref Expression
cbv2.1 (φ → Ⅎyψ)
cbv2.2 (φ → Ⅎxχ)
cbv2.3 (φ → (x = y → (ψχ)))
Assertion
Ref Expression
cbv2 (xyφ → (xψyχ))

Proof of Theorem cbv2
StepHypRef Expression
1 cbv2.1 . . 3 (φ → Ⅎyψ)
21nfrd 1763 . 2 (φ → (ψyψ))
3 cbv2.2 . . 3 (φ → Ⅎxχ)
43nfrd 1763 . 2 (φ → (χxχ))
5 cbv2.3 . 2 (φ → (x = y → (ψχ)))
62, 4, 5cbv2h 1980 1 (xyφ → (xψyχ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  wal 1540  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:  cbvald  2008
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