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Theorem hbxfrbi 1568
 Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. See hbxfreq 2456 for equality version. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypotheses
Ref Expression
hbxfrbi.1 (φψ)
hbxfrbi.2 (ψxψ)
Assertion
Ref Expression
hbxfrbi (φxφ)

Proof of Theorem hbxfrbi
StepHypRef Expression
1 hbxfrbi.2 . 2 (ψxψ)
2 hbxfrbi.1 . 2 (φψ)
32albii 1566 . 2 (xφxψ)
41, 2, 33imtr4i 257 1 (φxφ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557 This theorem depends on definitions:  df-bi 177 This theorem is referenced by:  hbe1w  1708  hbe1  1731  hbanOLD  1829  hb3anOLD  1831  hbex  1841  hbab1  2342  hbab  2344  cleqh  2450  hbxfreq  2456  hbral  2662  hbra1  2663
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