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Metamath Proof Explorer

Theorem 3eqtrd

Description: A deduction from three chained equalities. (Contributed by NM, 29-Oct-1995)

Ref Expression
Hypotheses 3eqtrd.1 
|- ( ph -> A = B )
3eqtrd.2 
|- ( ph -> B = C )
3eqtrd.3 
|- ( ph -> C = D )
Assertion 3eqtrd 
|- ( ph -> A = D )

Proof

Step Hyp Ref Expression
1 3eqtrd.1 
 |-  ( ph -> A = B )
2 3eqtrd.2 
 |-  ( ph -> B = C )
3 3eqtrd.3 
 |-  ( ph -> C = D )
4 2 3 eqtrd 
 |-  ( ph -> B = D )
5 1 4 eqtrd 
 |-  ( ph -> A = D )