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Theorem hblem 2127
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 1805 . 2 ([z / y]y Ax[z / y]y A)
3 clelsb3 2124 . 2 ([z / y]y Az A)
43albii 1339 . 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 1226   wcel 1374  [wsb 1627
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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-cleq 2015  df-clel 2018
This theorem is referenced by:  nfcrii  2153
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