Theorem bj-ssbid2 37009

Description: A special case of sbequ2 2261. (Contributed by BJ, 22-Dec-2020.)

Assertion

Ref	Expression
bj-ssbid2	⊢ ([𝑥 / 𝑥]𝜑 → 𝜑)

Proof of Theorem bj-ssbid2

Step	Hyp	Ref	Expression
1		equid 2019	. 2 ⊢ 𝑥 = 𝑥
2		sbequ2 2261	. 2 ⊢ (𝑥 = 𝑥 → ([𝑥 / 𝑥]𝜑 → 𝜑))
3	1, 2	ax-mp 5	1 ⊢ ([𝑥 / 𝑥]𝜑 → 𝜑)

Syntax hints:   → wi 4  [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  ax-12 2189

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

This theorem is referenced by: (None)