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Theorem sbidd 42214
Description: An identity theorem for substitution. See sbid 2099. 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 (𝜑𝜓)

Proof of Theorem sbidd
StepHypRef Expression
1 sbidd.1 . 2 (𝜑 → [𝑥 / 𝑥]𝜓)
2 sbid 2099 . 2 ([𝑥 / 𝑥]𝜓𝜓)
31, 2sylib 206 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  [wsb 1866
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-12 2033
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695  df-sb 1867
This theorem is referenced by: (None)
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