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Theorem cbvald 1797
Description: Deduction used to change bound variables, using implicit substitution, particularly useful in conjunction with dvelim 1890. (Contributed by NM, 2-Jan-2002.) (Revised by Mario Carneiro, 6-Oct-2016.) (Revised by Wolf Lammen, 13-May-2018.)
Hypotheses
Ref Expression
cbvald.1 yφ
cbvald.2 (φ → Ⅎyψ)
cbvald.3 (φ → (x = y → (ψχ)))
Assertion
Ref Expression
cbvald (φ → (xψyχ))
Distinct variable groups:   φ,x   χ,x
Allowed substitution hints:   φ(y)   ψ(x,y)   χ(y)

Proof of Theorem cbvald
StepHypRef Expression
1 nfv 1418 . 2 xφ
2 cbvald.1 . 2 yφ
3 cbvald.2 . 2 (φ → Ⅎyψ)
4 nfv 1418 . . 3 xχ
54a1i 9 . 2 (φ → Ⅎxχ)
6 cbvald.3 . 2 (φ → (x = y → (ψχ)))
71, 2, 3, 5, 6cbv2 1632 1 (φ → (xψyχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1240  wnf 1346
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  cbvaldva  1800
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