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Metamath Proof Explorer

Theorem uneq1d

Description: Deduction adding union to the right in a class equality. (Contributed by NM, 29-Mar-1998)

Ref Expression
Hypothesis uneq1d.1 
|- ( ph -> A = B )
Assertion uneq1d 
|- ( ph -> ( A u. C ) = ( B u. C ) )

Proof

Step Hyp Ref Expression
1 uneq1d.1 
 |-  ( ph -> A = B )
2 uneq1 
 |-  ( A = B -> ( A u. C ) = ( B u. C ) )
3 1 2 syl 
 |-  ( ph -> ( A u. C ) = ( B u. C ) )