Theorem sbeqal2i 44583

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 44582	. 2 ⊢ 𝑦 = 𝑧
3	2	eqcomi 2743	1 ⊢ 𝑧 = 𝑦

Syntax hints:

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-9 2123  ax-10 2146  ax-12 2182  ax-13 2374  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-ex 1781  df-nf 1785  df-sb 2068  df-cleq 2726

This theorem is referenced by: (None)