Theorem ax4 2225

Description: Rederivation of axiom ax-4 1631 from ax-c4 2215 and other older axioms. See axc4 1860 for the derivation of ax-c4 2215 from ax-4 1631. (Contributed by NM, 23-May-2008.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
ax4

Proof of Theorem ax4

Step	Hyp	Ref	Expression
1		ax-c4 2215	. . 3
2		ax-c5 2214	. . . 4
3		ax-c5 2214	. . . 4
4	2, 3	syl5 32	. . 3
5	1, 4	mpg 1620	. 2
6		ax-c4 2215	. 2
7	5, 6	syl 16	1

Syntax hints:  ->wi 4  A.wal 1393

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1618  ax-c5 2214  ax-c4 2215