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Theorem dvelimf 1869
Description: Version of dvelim 1871 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 1866 . 2 x x = y → ([y / z]φx[y / z]φ))
3 dvelimf.2 . . 3 (ψzψ)
4 dvelimf.3 . . 3 (z = y → (φψ))
53, 4sbieh 1651 . 2 ([y / z]φψ)
65albii 1335 . 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 1224  [wsb 1623
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 533  ax-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406
This theorem depends on definitions:  df-bi 110  df-nf 1326  df-sb 1624
This theorem is referenced by:  dvelim  1871  dveel1  1874  dveel2  1875
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