Theorem sbtALT 2106

Description: Alternate proof of sbt 2103, 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 2105	. 2 ⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
2		sbtALT.1	. 2 ⊢ 𝜑
3	1, 2	mpg 1830	1 ⊢ [𝑦 / 𝑥]𝜑

This proof depends on syntax axioms:  [wsb 2099

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-sb 2100

This theorem is used by: (None)