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Theorem nfriotadxy 5398
Description: Deduction version of nfriota 5399. (Contributed by Jim Kingdon, 12-Jan-2019.)
Hypotheses
Ref Expression
nfriotadxy.1 yφ
nfriotadxy.2 (φ → Ⅎxψ)
nfriotadxy.3 (φxA)
Assertion
Ref Expression
nfriotadxy (φx(y A ψ))
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)   ψ(x,y)   A(x,y)

Proof of Theorem nfriotadxy
StepHypRef Expression
1 df-riota 5391 . 2 (y A ψ) = (℩y(y A ψ))
2 nfriotadxy.1 . . 3 yφ
3 nfcv 2161 . . . . . 6 xy
43a1i 9 . . . . 5 (φxy)
5 nfriotadxy.3 . . . . 5 (φxA)
64, 5nfeld 2176 . . . 4 (φ → Ⅎx y A)
7 nfriotadxy.2 . . . 4 (φ → Ⅎxψ)
86, 7nfand 1444 . . 3 (φ → Ⅎx(y A ψ))
92, 8nfiotadxy 4795 . 2 (φx(℩y(y A ψ)))
101, 9nfcxfrd 2159 1 (φx(y A ψ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wnf 1329   wcel 1375  wnfc 2148  cio 4790  crio 5390
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 1364  ax-ie2 1365  ax-8 1377  ax-10 1378  ax-11 1379  ax-i12 1380  ax-bnd 1381  ax-4 1382  ax-17 1401  ax-i9 1405  ax-ial 1410  ax-i5r 1411  ax-ext 2005
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1629  df-clab 2010  df-cleq 2016  df-clel 2019  df-nfc 2150  df-rex 2289  df-sn 3355  df-uni 3554  df-iota 4792  df-riota 5391
This theorem is referenced by:  nfriota  5399
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