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Theorem dvelimf 1888
Description: Version of dvelim 1890 without any variable restrictions. (Contributed by NM, 1-Oct-2002.)
Hypotheses
Ref Expression
dvelimf.1 (φxφ)
dvelimf.2 (ψzψ)
dvelimf.3 (z = y → (φψ))
Assertion
Ref Expression
dvelimf x x = y → (ψxψ))

Proof of Theorem dvelimf
StepHypRef Expression
1 dvelimf.1 . . 3 (φxφ)
21hbsb4 1885 . 2 x x = y → ([y / z]φx[y / z]φ))
3 dvelimf.2 . . 3 (ψzψ)
4 dvelimf.3 . . 3 (z = y → (φψ))
53, 4sbieh 1670 . 2 ([y / z]φψ)
65albii 1356 . 2 (x[y / z]φxψ)
72, 5, 63imtr3g 193 1 x x = y → (ψxψ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 98  wal 1240  [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-in2 545  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:  dvelim  1890  dveel1  1893  dveel2  1894
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