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Theorem hblem 2142
 Description: Change the free variable of a hypothesis builder. (Contributed by NM, 5-Aug-1993.) (Revised by Andrew Salmon, 11-Jul-2011.)
Hypothesis
Ref Expression
hblem.1 (y Ax y A)
Assertion
Ref Expression
hblem (z Ax z A)
Distinct variable groups:   y,A   x,z
Allowed substitution hints:   A(x,z)

Proof of Theorem hblem
StepHypRef Expression
1 hblem.1 . . 3 (y Ax y A)
21hbsb 1820 . 2 ([z / y]y Ax[z / y]y A)
3 clelsb3 2139 . 2 ([z / y]y Az A)
43albii 1356 . 2 (x[z / y]y Ax z A)
52, 3, 43imtr3i 189 1 (z Ax z A)
 Colors of variables: wff set class Syntax hints:   → wi 4  ∀wal 1240   ∈ wcel 1390  [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  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033 This theorem is referenced by:  nfcrii  2168
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