Theorem axc4 1860

Description: Show that the original axiom ax-c4 2215 can be derived from ax-4 1631 and others. See ax4 2225 for the rederivation of ax-4 1631 from ax-c4 2215.

Part of the proof is based on the proof of Lemma 22 of [Monk2] p. 114. (Contributed by NM, 21-May-2008.) (Proof modification is discouraged.)

Assertion

Ref	Expression
axc4

Proof of Theorem axc4

Step	Hyp	Ref	Expression
1		sp 1859	. . . 4
2	1	con2i 120	. . 3
3		hbn1 1838	. . 3
4		hbn1 1838	. . . . 5
5	4	con1i 129	. . . 4
6	5	alimi 1633	. . 3
7	2, 3, 6	3syl 20	. 2
8		alim 1632	. 2
9	7, 8	syl5 32	1

Syntax hints:  -.wn 3  ->wi 4  A.wal 1393

This theorem is referenced by:  axc5c4c711  31308

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854

This theorem depends on definitions:  df-bi 185  df-ex 1613