Theorem bj-ssbid1 36181

Description: A special case of sbequ1 2235. (Contributed by BJ, 22-Dec-2020.)

Assertion

Ref	Expression
bj-ssbid1	⊢ (𝜑 → [𝑥 / 𝑥]𝜑)

Proof of Theorem bj-ssbid1

Step	Hyp	Ref	Expression
1		equid 2007	. 2 ⊢ 𝑥 = 𝑥
2		sbequ1 2235	. 2 ⊢ (𝑥 = 𝑥 → (𝜑 → [𝑥 / 𝑥]𝜑))
3	1, 2	ax-mp 5	1 ⊢ (𝜑 → [𝑥 / 𝑥]𝜑)

Syntax hints:   → wi 4  [wsb 2059

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-12 2166

This theorem depends on definitions:  df-bi 206  df-an 395  df-ex 1774  df-sb 2060

This theorem is referenced by: (None)