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Step * 2 of Lemma rnonzero_functionality


1. ∀x,y:ℝ.  ((x = y) ⇒ rnonzero(x) ⇒ rnonzero(y))
⊢ ∀x,y:ℝ.  ((x = y) ⇒ (rnonzero(x) ⇐⇒ rnonzero(y)))
BY
{ (Auto THEN InstHyp [⌜y⌝;⌜x⌝] 1 ⋅ THEN Auto) }

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Latex:

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Latex:

1.  \mforall{}x,y:\mBbbR{}.    ((x  =  y)  {}\mRightarrow{}  rnonzero(x)  {}\mRightarrow{}  rnonzero(y))
\mvdash{}  \mforall{}x,y:\mBbbR{}.    ((x  =  y)  {}\mRightarrow{}  (rnonzero(x)  \mLeftarrow{}{}\mRightarrow{}  rnonzero(y)))


By

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Latex:
(Auto  THEN  InstHyp  [\mkleeneopen{}y\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{}]  1  \mcdot{}  THEN  Auto)

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