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Theorem nfsbd 1848
Description: Deduction version of nfsb 1819. (Contributed by NM, 15-Feb-2013.)
Hypotheses
Ref Expression
nfsbd.1 xφ
nfsbd.2 (φ → Ⅎzψ)
Assertion
Ref Expression
nfsbd (φ → Ⅎz[y / x]ψ)
Distinct variable group:   y,z
Allowed substitution hints:   φ(x,y,z)   ψ(x,y,z)

Proof of Theorem nfsbd
StepHypRef Expression
1 nfsbd.1 . . 3 xφ
21nfri 1409 . 2 (φxφ)
3 nfsbd.2 . . 3 (φ → Ⅎzψ)
43alimi 1341 . 2 (xφxzψ)
5 nfsbt 1847 . 2 (xzψ → Ⅎz[y / x]ψ)
62, 4, 53syl 17 1 (φ → Ⅎz[y / x]ψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240  wnf 1346  [wsb 1642
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
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643
This theorem is referenced by:  nfeud  1913  nfabd  2193  nfraldya  2352  nfrexdya  2353  cbvrald  9262
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