Theorem id1 23

Description: Alternate proof of id 22. 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.appstate.edu/~hirstjl/primer/hirst.pdf. Note that the second occurrence of in Steps 1 to 4 and the sixth in Step 3 may simultaneously be replaced by any wff , which may ease the understanding of the proof. For a shorter version of the proof that takes advantage of previously proved theorems, see id 22. (Contributed by NM, 30-Sep-1992.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
id1

Proof of Theorem id1

Step	Hyp	Ref	Expression
1		ax-1 6	. 2
2		ax-1 6	. . 3
3		ax-2 7	. . 3
4	2, 3	ax-mp 5	. 2
5	1, 4	ax-mp 5	1

Syntax hints:  ->wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7