Nuprl Lemma : guard_functionality_wrt_iff
∀p,q:ℙ.  ({p 
⇐⇒ q} 
⇒ {{p} 
⇐⇒ {q}})
Proof
Definitions occuring in Statement : 
prop: ℙ
, 
guard: {T}
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
implies: P 
⇒ Q
Definitions unfolded in proof : 
guard: {T}
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
member: t ∈ T
, 
prop: ℙ
, 
uall: ∀[x:A]. B[x]
Latex:
\mforall{}p,q:\mBbbP{}.    (\{p  \mLeftarrow{}{}\mRightarrow{}  q\}  {}\mRightarrow{}  \{\{p\}  \mLeftarrow{}{}\mRightarrow{}  \{q\}\})
Date html generated:
2016_05_17-AM-10_07_17
Last ObjectModification:
2015_12_29-PM-03_51_01
Theory : classrel!lemmas
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