Theorem sbidd 46420

Description: An identity theorem for substitution. See sbid 2248. See Remark 9.1 in [Megill] p. 447 (p. 15 of the preprint). (Contributed by DAW, 18-Feb-2017.)

Hypothesis

Ref	Expression
sbidd.1	⊢ (𝜑 → [𝑥 / 𝑥]𝜓)

Assertion

Ref	Expression
sbidd	⊢ (𝜑 → 𝜓)

Proof of Theorem sbidd

Step	Hyp	Ref	Expression
1		sbidd.1	. 2 ⊢ (𝜑 → [𝑥 / 𝑥]𝜓)
2		sbid 2248	. 2 ⊢ ([𝑥 / 𝑥]𝜓 ↔ 𝜓)
3	1, 2	sylib 217	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  [wsb 2067

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-12 2171

This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1783  df-sb 2068

This theorem is referenced by: (None)