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Theorem bnj1113 29133
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 3944 1  |-  ( A  =  B  ->  U_ x  e.  C  E  =  U_ x  e.  D  E
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632   U_ciun 3921
This theorem is referenced by:  bnj106  29216  bnj155  29227  bnj222  29231  bnj540  29240  bnj553  29246  bnj611  29266  bnj893  29276  bnj966  29292  bnj1112  29329
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-v 2803  df-in 3172  df-ss 3179  df-iun 3923
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