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Theorem frege58bid 40126
Description: If 𝑥𝜑 is affirmed, 𝜑 cannot be denied. Identical to sp 2172. See ax-frege58b 40125 and frege58c 40145 for versions which more closely track the original. Axiom 58 of [Frege1879] p. 51. (Contributed by RP, 28-Mar-2020.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege58bid (∀𝑥𝜑𝜑)

Proof of Theorem frege58bid
StepHypRef Expression
1 ax-frege58b 40125 . 2 (∀𝑥𝜑 → [𝑥 / 𝑥]𝜑)
2 sbid 2247 . . 3 ([𝑥 / 𝑥]𝜑𝜑)
32biimpi 217 . 2 ([𝑥 / 𝑥]𝜑𝜑)
41, 3syl 17 1 (∀𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1526  [wsb 2060
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-12 2167  ax-frege58b 40125
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-sb 2061
This theorem is referenced by: (None)
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