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Theorem ee11an 28767
Description: e11an 28766 without virtual deductions. syl22anc 1183 is also e11an 28766 without virtual deductions, exept with a different order of hypotheses. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee11an.1  |-  ( ph  ->  ps )
ee11an.2  |-  ( ph  ->  ch )
ee11an.3  |-  ( ( ps  /\  ch )  ->  th )
Assertion
Ref Expression
ee11an  |-  ( ph  ->  th )

Proof of Theorem ee11an
StepHypRef Expression
1 ee11an.1 . 2  |-  ( ph  ->  ps )
2 ee11an.2 . 2  |-  ( ph  ->  ch )
3 ee11an.3 . . 3  |-  ( ( ps  /\  ch )  ->  th )
43ex 423 . 2  |-  ( ps 
->  ( ch  ->  th )
)
51, 2, 4sylc 56 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
  Copyright terms: Public domain W3C validator