Theorem bj-ssbid2 31834

Description: A special case of bj-ssbequ2 31832. (Contributed by BJ, 22-Dec-2020.)

Assertion

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

Proof of Theorem bj-ssbid2

Step	Hyp	Ref	Expression
1		equid 1926	. 2 ⊢ 𝑥 = 𝑥
2		bj-ssbequ2 31832	. 2 ⊢ (𝑥 = 𝑥 → ([𝑥/𝑥]b𝜑 → 𝜑))
3	1, 2	ax-mp 5	1 ⊢ ([𝑥/𝑥]b𝜑 → 𝜑)

Syntax hints:   → wi 4  [wssb 31808

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-ssb 31809

This theorem is referenced by: (None)