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Theorem nfriotadxy 5416
Description: Deduction version of nfriota 5417. (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 5409 . 2 (y A ψ) = (℩y(y A ψ))
2 nfriotadxy.1 . . 3 yφ
3 nfcv 2175 . . . . . 6 xy
43a1i 9 . . . . 5 (φxy)
5 nfriotadxy.3 . . . . 5 (φxA)
64, 5nfeld 2190 . . . 4 (φ → Ⅎx y A)
7 nfriotadxy.2 . . . 4 (φ → Ⅎxψ)
86, 7nfand 1457 . . 3 (φ → Ⅎx(y A ψ))
92, 8nfiotadxy 4812 . 2 (φx(℩y(y A ψ)))
101, 9nfcxfrd 2173 1 (φx(y A ψ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wnf 1346   wcel 1390  wnfc 2162  cio 4807  crio 5408
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-sn 3372  df-uni 3571  df-iota 4809  df-riota 5409
This theorem is referenced by:  nfriota  5417
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