Theorem sbtALT 2080

Description: Alternate proof of sbt 2077, shorter but using additional axioms. (Contributed by NM, 21-Jan-2004.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
sbtALT.1	⊢ 𝜑

Assertion

Ref	Expression
sbtALT	⊢ [𝑦 / 𝑥]𝜑

Proof of Theorem sbtALT

Step	Hyp	Ref	Expression
1		stdpc4 2079	. 2 ⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
2		sbtALT.1	. 2 ⊢ 𝜑
3	1, 2	mpg 1804	1 ⊢ [𝑦 / 𝑥]𝜑

Syntax hints:  [wsb 2073

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015

This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1787  df-sb 2074

This theorem is referenced by: (None)