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Theorem hbim1 1459
Description: A closed form of hbim 1434. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
hbim1.1 (φxφ)
hbim1.2 (φ → (ψxψ))
Assertion
Ref Expression
hbim1 ((φψ) → x(φψ))

Proof of Theorem hbim1
StepHypRef Expression
1 hbim1.2 . . 3 (φ → (ψxψ))
21a2i 11 . 2 ((φψ) → (φxψ))
3 hbim1.1 . . 3 (φxφ)
4319.21h 1446 . 2 (x(φψ) ↔ (φxψ))
52, 4sylibr 137 1 ((φψ) → x(φψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  nfim1  1460  sbco2d  1837  sbco2vd  1838
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