Theorem sbidd-misc 48043

Description: An identity theorem for substitution. See sbid 2239. See Remark 9.1 in [Megill] p. 447 (p. 15 of the preprint). (Contributed by DAW, 18-Feb-2017.)

Assertion

Ref	Expression
sbidd-misc	⊢ ((𝜑 → [𝑥 / 𝑥]𝜓) ↔ (𝜑 → 𝜓))

Proof of Theorem sbidd-misc

Step	Hyp	Ref	Expression
1		sbid 2239	. 2 ⊢ ([𝑥 / 𝑥]𝜓 ↔ 𝜓)
2	1	imbi2i 336	1 ⊢ ((𝜑 → [𝑥 / 𝑥]𝜓) ↔ (𝜑 → 𝜓))

Syntax hints:   → wi 4   ↔ wb 205  [wsb 2059

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-12 2163

This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1774  df-sb 2060

This theorem is referenced by: (None)