Theorem sbt 2407

Description: A substitution into a theorem yields a theorem. (See chvar 2250 and chvarv 2251 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 2341	. 2 ⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
2		sbt.1	. 2 ⊢ 𝜑
3	1, 2	mpg 1715	1 ⊢ [𝑦 / 𝑥]𝜑

Syntax hints:  [wsb 1867

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034  ax-13 2234

This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-sb 1868

This theorem is referenced by:  vjust  3174  iscatd2  16165  iuninc  28761  suppss2f  28819  esumpfinvalf  29465  sbtT  37804  2sb5ndVD  38168  2sb5ndALT  38190