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Theorem r19.37 2651
 Description: Restricted version of one direction of Theorem 19.37 of [Margaris] p. 90. (The other direction doesn't hold when is empty.) (Contributed by FL, 13-May-2012.) (Revised by Mario Carneiro, 11-Dec-2016.)
Hypothesis
Ref Expression
r19.37.1
Assertion
Ref Expression
r19.37

Proof of Theorem r19.37
StepHypRef Expression
1 r19.35 2649 . 2
2 r19.37.1 . . . 4
3 ax-1 7 . . . 4
42, 3ralrimi 2586 . . 3
54imim1i 56 . 2
61, 5sylbi 189 1
 Colors of variables: wff set class Syntax hints:   wi 6  wnf 1539   wcel 1621  wral 2509  wrex 2510 This theorem is referenced by:  r19.37av  2652 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-17 1628  ax-4 1692 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-ral 2513  df-rex 2514
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