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Theorem cbvriotav 5403
Description: Change bound variable in a restricted description binder. (Contributed by NM, 18-Mar-2013.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypothesis
Ref Expression
cbvriotav.1 (x = y → (φψ))
Assertion
Ref Expression
cbvriotav (x A φ) = (y A ψ)
Distinct variable groups:   x,A   y,A   φ,y   ψ,x
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem cbvriotav
StepHypRef Expression
1 nfv 1402 . 2 yφ
2 nfv 1402 . 2 xψ
3 cbvriotav.1 . 2 (x = y → (φψ))
41, 2, 3cbvriota 5402 1 (x A φ) = (y A ψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = wceq 1228  crio 5392
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-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-rex 2290  df-sn 3356  df-uni 3555  df-iota 4794  df-riota 5393
This theorem is referenced by: (None)
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