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Theorem ee21 1365
Description: e21 28505 without virtual deductions. (Contributed by Alan Sare, 18-Mar-2012.) (New usage is discouraged.) TODO: decide if this is worth keeping.
Hypotheses
Ref Expression
ee21.1  |-  ( ph  ->  ( ps  ->  ch ) )
ee21.2  |-  ( ph  ->  th )
ee21.3  |-  ( ch 
->  ( th  ->  ta ) )
Assertion
Ref Expression
ee21  |-  ( ph  ->  ( ps  ->  ta ) )

Proof of Theorem ee21
StepHypRef Expression
1 ee21.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 ee21.2 . . 3  |-  ( ph  ->  th )
32a1d 22 . 2  |-  ( ph  ->  ( ps  ->  th )
)
4 ee21.3 . 2  |-  ( ch 
->  ( th  ->  ta ) )
51, 3, 4ee22 1352 1  |-  ( ph  ->  ( ps  ->  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  omeulem2  6581  btwnconn1lem12  24721  sbcim2g  28302  ee21an  28507
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator