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Theorem alrimd 1574
Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
alrimd.1  |-  F/ x ph
alrimd.2  |-  F/ x ps
alrimd.3  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
alrimd  |-  ( ph  ->  ( ps  ->  A. x ch ) )

Proof of Theorem alrimd
StepHypRef Expression
1 alrimd.1 . 2  |-  F/ x ph
2 alrimd.2 . . 3  |-  F/ x ps
32a1i 9 . 2  |-  ( ph  ->  F/ x ps )
4 alrimd.3 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
51, 3, 4alrimdd 1573 1  |-  ( ph  ->  ( ps  ->  A. x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1314   F/wnf 1421
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-5 1408  ax-gen 1410  ax-4 1472
This theorem depends on definitions:  df-bi 116  df-nf 1422
This theorem is referenced by:  euexex  2062  ralrimd  2487  fiintim  6785
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