Theorem sbeqal2i 45138

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 45137	. 2 ⊢ 𝑦 = 𝑧
3	2	eqcomi 2771	1 ⊢ 𝑧 = 𝑦

This proof depends on syntax axioms:

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-9 2152  ax-10 2175  ax-12 2212  ax-13 2403  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-ex 1809  df-nf 1813  df-sb 2096  df-cleq 2754

This theorem is used by: (None)