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Theorem pm2.61 124
Description: Theorem *2.61 of [WhiteheadRussell] p. 107. Useful for eliminating an antecedent. (The proof was shortened by O'Cat, 19-Feb-2008.)
Assertion
Ref Expression
pm2.61 |- ((ph -> ps) -> ((-. ph -> ps) -> ps))
Proof of Theorem pm2.61
StepHypRef Expression
1 con1 92 . . 3 |- ((-. ph -> ps) -> (-. ps -> ph))
21imim1d 28 . 2 |- ((-. ph -> ps) -> ((ph -> ps) -> (-. ps -> ps)))
3 pm2.18 81 . 2 |- ((-. ps -> ps) -> ps)
42, 3syl6com 53 1 |- ((ph -> ps) -> ((-. ph -> ps) -> ps))
Colors of variables: wff set class
Syntax hints:  -. wn 2   -> wi 3
This theorem is referenced by:  pm2.61i 126  pm2.6 133  pm5.18 658  undif4 2315
This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7
Copyright terms: Public domain