Theorem bj-ssbid2 37325

Description: A special case of sbequ2 2288. (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 2045	. 2 ⊢ 𝑥 = 𝑥
2		sbequ2 2288	. 2 ⊢ (𝑥 = 𝑥 → ([𝑥 / 𝑥]𝜑 → 𝜑))
3	1, 2	ax-mp 5	1 ⊢ ([𝑥 / 𝑥]𝜑 → 𝜑)

This proof depends on syntax axioms:   → wi 4  [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  ax-12 2216

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

This theorem is used by: (None)