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Metamath Proof Explorer

Theorem id

Description: Principle of identity. Theorem *2.08 of WhiteheadRussell p. 101. For another version of the proof directly from axioms, see idALT . Its associated inference, idi , requires no axioms for its proof, contrary to id . Note that the second occurrences of ph in Steps 1 and 2 may be simultaneously replaced by any wff ps , which may ease the understanding of the proof. (Contributed by NM, 29-Dec-1992) (Proof shortened by Stefan Allan, 20-Mar-2006)

Ref Expression
Assertion id 
|- ( ph -> ph )

Proof

Step Hyp Ref Expression
1 ax-1 
 |-  ( ph -> ( ph -> ph ) )
2 ax-1 
 |-  ( ph -> ( ( ph -> ph ) -> ph ) )
3 1 2 mpd 
 |-  ( ph -> ph )