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Theorem bnj1113 28817
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1113.1  |-  ( A  =  B  ->  C  =  D )
Assertion
Ref Expression
bnj1113  |-  ( A  =  B  ->  U_ x  e.  C  E  =  U_ x  e.  D  E
)
Distinct variable groups:    x, C    x, D
Allowed substitution hints:    A( x)    B( x)    E( x)

Proof of Theorem bnj1113
StepHypRef Expression
1 bnj1113.1 . 2  |-  ( A  =  B  ->  C  =  D )
21iuneq1d 3928 1  |-  ( A  =  B  ->  U_ x  e.  C  E  =  U_ x  e.  D  E
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623   U_ciun 3905
This theorem is referenced by:  bnj106  28900  bnj155  28911  bnj222  28915  bnj540  28924  bnj553  28930  bnj611  28950  bnj893  28960  bnj966  28976  bnj1112  29013
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-v 2790  df-in 3159  df-ss 3166  df-iun 3907
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