Theorem equsb3rOLD 2111

Description: Obsolete version of equsb3r 2110 as of 2-Sep-2023. (Contributed by AV, 29-Jul-2023.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
equsb3rOLD	⊢ ([𝑦 / 𝑥]𝑧 = 𝑥 ↔ 𝑧 = 𝑦)

Distinct variable group:   𝑥,𝑧

Proof of Theorem equsb3rOLD

Step	Hyp	Ref	Expression
1		equcom 2025	. . 3 ⊢ (𝑧 = 𝑥 ↔ 𝑥 = 𝑧)
2	1	sbbii 2081	. 2 ⊢ ([𝑦 / 𝑥]𝑧 = 𝑥 ↔ [𝑦 / 𝑥]𝑥 = 𝑧)
3		equsb3 2109	. 2 ⊢ ([𝑦 / 𝑥]𝑥 = 𝑧 ↔ 𝑦 = 𝑧)
4		equcom 2025	. 2 ⊢ (𝑦 = 𝑧 ↔ 𝑧 = 𝑦)
5	2, 3, 4	3bitri 299	1 ⊢ ([𝑦 / 𝑥]𝑧 = 𝑥 ↔ 𝑧 = 𝑦)

Syntax hints:   ↔ wb 208  [wsb 2069

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 1970  ax-7 2015

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1781  df-sb 2070

This theorem is referenced by: (None)