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Theorem drsb2 2269
Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint). (Contributed by NM, 27-Feb-2005.)
Assertion
Ref Expression
drsb2 (∀𝑥 𝑥 = 𝑦 → ([𝑥 / 𝑧]𝜑 ↔ [𝑦 / 𝑧]𝜑))

Proof of Theorem drsb2
StepHypRef Expression
1 sbequ 2091 . 2 (𝑥 = 𝑦 → ([𝑥 / 𝑧]𝜑 ↔ [𝑦 / 𝑧]𝜑))
21sps 2186 1 (∀𝑥 𝑥 = 𝑦 → ([𝑥 / 𝑧]𝜑 ↔ [𝑦 / 𝑧]𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wal 1536  [wsb 2070
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-12 2179
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2071
This theorem is referenced by:  sbcom3  2550  sbal2OLD  2576
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