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Theorem hblem 2457
 Description: Change the free variable of a hypothesis builder. Lemma for nfcrii 2482. (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 2110 . 2 ([z / y]y Ax[z / y]y A)
3 clelsb3 2455 . 2 ([z / y]y Az A)
43albii 1566 . 2 (x[z / y]y Ax z A)
52, 3, 43imtr3i 256 1 (z Ax z A)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540  [wsb 1648   ∈ wcel 1710 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349 This theorem is referenced by:  nfcrii  2482
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