Theorem eqtrid 2210

Description: An equality transitivity deduction. (Contributed by NM, 21-Jun-1993.)

Hypotheses

Ref	Expression
eqtrid.1	|- A = B
eqtrid.2	|- ( ph -> B = C )

Assertion

Ref	Expression
eqtrid	|- ( ph -> A = C )

Proof of Theorem eqtrid

Step	Hyp	Ref	Expression
1		eqtrid.1	. . 3 |- A = B
2	1	a1i 9	. 2 |- ( ph -> A = B )
3		eqtrid.2	. 2 |- ( ph -> B = C )
4	2, 3	eqtrd 2198	1 |- ( ph -> A = C )

Syntax hints:   -> wi 4   = wceq 1343

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-4 1498  ax-17 1514  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-cleq 2158

This theorem is referenced by:  mgm1  12601  grpidvalg  12604