Theorem equtr2 1133

Description: A transitive law for equality.

Assertion

Ref	Expression
equtr2	|- ((x = z /\ y = z) -> x = y)

Proof of Theorem equtr2

Step	Hyp	Ref	Expression
1		equtr 1131	. . 3 |- (x = z -> (z = y -> x = y))
2		equcomi 1128	. . 3 |- (y = z -> z = y)
3	1, 2	syl5 21	. 2 |- (x = z -> (y = z -> x = y))
4	3	imp 350	1 |- ((x = z /\ y = z) -> x = y)

Syntax hints:   -> wi 3   /\ wa 223   = wceq 956

This theorem is referenced by:  mo 1393  2mo 1447

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-8 964  ax-12 968  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123

This theorem depends on definitions:  df-bi 147  df-an 225

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