Theorem sbeqal2i 38600

Description: If x = y implies x = z, then we can infer z = y. (Contributed by Andrew Salmon, 3-Jun-2011.)

Hypothesis

Ref	Expression
sbeqal1i.1	|- ( x = y -> x = z )

Assertion

Ref	Expression
sbeqal2i	|- z = y

Distinct variable group:   x, z

Proof of Theorem sbeqal2i

Step	Hyp	Ref	Expression
1		sbeqal1i.1	. . 3 |- ( x = y -> x = z )
2	1	sbeqal1i 38599	. 2 |- y = z
3	2	eqcomi 2631	1 |- z = y

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-sb 1881  df-cleq 2615

This theorem is referenced by: (None)