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Theorem a2i 11
Description: Inference derived from axiom ax-2 7. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
a2i.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
a2i  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ch )
)

Proof of Theorem a2i
StepHypRef Expression
1 a2i.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 ax-2 7 . 2  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( ph  ->  ps )  ->  ( ph  ->  ch ) ) )
31, 2ax-mp 5 1  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-2 7
This theorem is referenced by:  imim2i  12  mpd  13  sylcom  28  pm2.43  53  ancl  316  ancr  319  anc2r  326  pm2.65  648  pm2.18dc  840  con4biddc  842  hbim1  1549  sbcof2  1782  ralimia  2493  ceqsalg  2714  rspct  2782  elabgt  2825  fvmptt  5512  ordiso2  6920  bj-exlimmp  13006  bj-rspgt  13023  bj-indint  13159
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