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Theorem bnj1113 29218
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 4118 1  |-  ( A  =  B  ->  U_ x  e.  C  E  =  U_ x  e.  D  E
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1653   U_ciun 4095
This theorem is referenced by:  bnj106  29301  bnj222  29316  bnj540  29325  bnj553  29331  bnj611  29351  bnj966  29377  bnj1112  29414
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-v 2960  df-in 3329  df-ss 3336  df-iun 4097
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