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Theorem sbequOLD 2065
 Description: Obsolete proof of sbequ 2063 as of 7-Jul-2023. An equality theorem for substitution. Used in proof of Theorem 9.7 in [Megill] p. 449 (p. 16 of the preprint). (Contributed by NM, 14-May-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sbequOLD (𝑥 = 𝑦 → ([𝑥 / 𝑧]𝜑 ↔ [𝑦 / 𝑧]𝜑))

Proof of Theorem sbequOLD
StepHypRef Expression
1 sbequi 2064 . 2 (𝑥 = 𝑦 → ([𝑥 / 𝑧]𝜑 → [𝑦 / 𝑧]𝜑))
2 sbequi 2064 . . 3 (𝑦 = 𝑥 → ([𝑦 / 𝑧]𝜑 → [𝑥 / 𝑧]𝜑))
32equcoms 2004 . 2 (𝑥 = 𝑦 → ([𝑦 / 𝑧]𝜑 → [𝑥 / 𝑧]𝜑))
41, 3impbid 213 1 (𝑥 = 𝑦 → ([𝑥 / 𝑧]𝜑 ↔ [𝑦 / 𝑧]𝜑))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 207  [wsb 2042 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992 This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1762  df-sb 2043 This theorem is referenced by: (None)
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