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Theorem id1 20
Description: Principle of identity. Theorem *2.08 of [WhiteheadRussell] p. 101. This version is proved directly from the axioms for demonstration purposes. This proof is a popular example in the literature and is identical, step for step, to the proofs of Theorem 1 of [Margaris] p. 51, Example 2.7(a) of [Hamilton] p. 31, Lemma 10.3 of [BellMachover] p. 36, and Lemma 1.8 of [Mendelson] p. 36. It is also "Our first proof" in Hirst and Hirst's A Primer for Logic and Proof p. 17 (PDF p. 23) at http://www.mathsci.appstate.edu/~hirstjl/primer/hirst.pdf. For a shorter version of the proof that takes advantage of previously proved theorems, see id 19. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
id1

Proof of Theorem id1
StepHypRef Expression
1 ax-1 5 . 2
2 ax-1 5 . . 3
3 ax-2 6 . . 3
42, 3ax-mp 8 . 2
51, 4ax-mp 8 1
Colors of variables: wff set class
Syntax hints:   wi 4
This theorem is referenced by:  eqer  5981  erdmrn  5985  nnltp1c  6271  spacis  6288  nchoicelem1  6289  nchoicelem2  6290
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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