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Theorem cbv3h 1628
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 12-May-2018.)
Hypotheses
Ref Expression
cbv3h.1 (φyφ)
cbv3h.2 (ψxψ)
cbv3h.3 (x = y → (φψ))
Assertion
Ref Expression
cbv3h (xφyψ)

Proof of Theorem cbv3h
StepHypRef Expression
1 cbv3h.1 . . 3 (φyφ)
21nfi 1348 . 2 yφ
3 cbv3h.2 . . 3 (ψxψ)
43nfi 1348 . 2 xψ
5 cbv3h.3 . 2 (x = y → (φψ))
62, 4, 5cbv3 1627 1 (xφyψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240
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-4 1397  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  cbvalh  1633  ax16  1691  ax16i  1735  cleqh  2134
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