Theorem 3eqtr4aOLD 1955

Description: A chained equality inference, useful for converting to definitions.

Hypotheses

Ref	Expression
3eqtr4a.1	|- A = B
3eqtr4a.2	|- (ph -> C = A)
3eqtr4a.3	|- (ph -> D = B)

Assertion

Ref	Expression
3eqtr4aOLD	|- (ph -> C = D)

Proof of Theorem 3eqtr4aOLD

Step	Hyp	Ref	Expression
1		3eqtr4a.1	. . 3 |- A = B
2	1	a1i 8	. 2 |- (ph -> A = B)
3		3eqtr4a.2	. 2 |- (ph -> C = A)
4		3eqtr4a.3	. 2 |- (ph -> D = B)
5	2, 3, 4	3eqtr4d 1937	1 |- (ph -> C = D)

Syntax hints:   -> wi 3   = wceq 1298

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-17 1317  ax-4 1319  ax-5o 1321  ax-ext 1865

This theorem depends on definitions:  df-bi 164  df-an 242  df-cleq 1877

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