Theorem bj-ssbid2 36604

Description: A special case of sbequ2 2248. (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 2010	. 2 ⊢ 𝑥 = 𝑥
2		sbequ2 2248	. 2 ⊢ (𝑥 = 𝑥 → ([𝑥 / 𝑥]𝜑 → 𝜑))
3	1, 2	ax-mp 5	1 ⊢ ([𝑥 / 𝑥]𝜑 → 𝜑)

Syntax hints:   → wi 4  [wsb 2063

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-12 2176

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-sb 2064

This theorem is referenced by: (None)