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Theorem e10an 28468
Description: Conjunction form of e10 28467. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e10an.1  |-  (. ph  ->.  ps
).
e10an.2  |-  ch
e10an.3  |-  ( ( ps  /\  ch )  ->  th )
Assertion
Ref Expression
e10an  |-  (. ph  ->.  th
).

Proof of Theorem e10an
StepHypRef Expression
1 e10an.1 . 2  |-  (. ph  ->.  ps
).
2 e10an.2 . 2  |-  ch
3 e10an.3 . . 3  |-  ( ( ps  /\  ch )  ->  th )
43ex 423 . 2  |-  ( ps 
->  ( ch  ->  th )
)
51, 2, 4e10 28467 1  |-  (. ph  ->.  th
).
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   (.wvd1 28337
This theorem is referenced by:  snsslVD  28604
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  df-vd1 28338
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