Theorem sbt 2419

Description: A substitution into a theorem yields a theorem. (See chvar 2262 and chvarv 2263 for versions using implicit substitution.) (Contributed by NM, 21-Jan-2004.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 20-Jul-2018.)

Hypothesis

Ref	Expression
sbt.1	⊢ 𝜑

Assertion

Ref	Expression
sbt	⊢ [𝑦 / 𝑥]𝜑

Proof of Theorem sbt

Step	Hyp	Ref	Expression
1		stdpc4 2353	. 2 ⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
2		sbt.1	. 2 ⊢ 𝜑
3	1, 2	mpg 1724	1 ⊢ [𝑦 / 𝑥]𝜑

Syntax hints:  [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-sb 1881

This theorem is referenced by:  vjust  3201  iscatd2  16342  iuninc  29379  suppss2f  29439  esumpfinvalf  30138  sbtT  38783  2sb5ndVD  39146  2sb5ndALT  39168