Theorem sbeqal2i 44914

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 44913	. 2 ⊢ 𝑦 = 𝑧
3	2	eqcomi 2761	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 1805  ax-4 1819  ax-5 1920  ax-6 1977  ax-7 2018  ax-9 2142  ax-10 2165  ax-12 2202  ax-13 2393  ax-ext 2724

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 857  df-ex 1790  df-nf 1794  df-sb 2081  df-cleq 2744

This theorem is referenced by: (None)