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Axiom ax-io 640
Description: Definition of 'or'. One of the axioms of propositional logic. (Contributed by Mario Carneiro, 31-Jan-2015.) Use its alias jaob 641 instead. (New usage is discouraged.)
Assertion
Ref Expression
ax-io  |-  ( ( ( ph  \/  ch )  ->  ps )  <->  ( ( ph  ->  ps )  /\  ( ch  ->  ps )
) )

Detailed syntax breakdown of Axiom ax-io
StepHypRef Expression
1 wph . . . 4  wff  ph
2 wch . . . 4  wff  ch
31, 2wo 639 . . 3  wff  ( ph  \/  ch )
4 wps . . 3  wff  ps
53, 4wi 4 . 2  wff  ( (
ph  \/  ch )  ->  ps )
61, 4wi 4 . . 3  wff  ( ph  ->  ps )
72, 4wi 4 . . 3  wff  ( ch 
->  ps )
86, 7wa 101 . 2  wff  ( (
ph  ->  ps )  /\  ( ch  ->  ps )
)
95, 8wb 102 1  wff  ( ( ( ph  \/  ch )  ->  ps )  <->  ( ( ph  ->  ps )  /\  ( ch  ->  ps )
) )
Colors of variables: wff set class
This axiom is referenced by:  jaob  641
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