Theorem hbae-o 2232

Description: All variables are effectively bound in an identical variable specifier. Version of hbae 2055 using ax-c11 2218. (Contributed by NM, 13-May-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
hbae-o

Proof of Theorem hbae-o

Step	Hyp	Ref	Expression
1		ax-c5 2214	. . . . 5
2		ax-c9 2221	. . . . 5
3	1, 2	syl7 68	. . . 4
4		ax-c11 2218	. . . . 5
5	4	aecoms-o 2231	. . . 4
6		ax-c11 2218	. . . . . . 7
7	6	pm2.43i 47	. . . . . 6
8		ax-c11 2218	. . . . . 6
9	7, 8	syl5 32	. . . . 5
10	9	aecoms-o 2231	. . . 4
11	3, 5, 10	pm2.61ii 165	. . 3
12	11	axc4i-o 2229	. 2
13		ax-11 1842	. 2
14	12, 13	syl 16	1

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

This theorem is referenced by:  dral1-o  2233  hbnae-o  2258  dral2-o  2260  aev-o  2261

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-11 1842  ax-c5 2214  ax-c4 2215  ax-c7 2216  ax-c11 2218  ax-c9 2221

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