Theorem hbae 2055

Description: All variables are effectively bound in an identical variable specifier. (Contributed by NM, 13-May-1993.) (Proof shortened by Wolf Lammen, 21-Apr-2018.)

Assertion

Ref	Expression
hbae

Proof of Theorem hbae

Step	Hyp	Ref	Expression
1		sp 1859	. . . . 5
2		axc9 2046	. . . . 5
3	1, 2	syl7 68	. . . 4
4		axc112 1937	. . . 4
5		axc11 2054	. . . . . 6
6	5	pm2.43i 47	. . . . 5
7		axc112 1937	. . . . 5
8	6, 7	syl5 32	. . . 4
9	3, 4, 8	pm2.61ii 165	. . 3
10	9	axc4i 1898	. 2
11		ax-11 1842	. 2
12	10, 11	syl 16	1

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

This theorem is referenced by:  nfae  2056  hbnae  2057  aevALT  2063  drex2  2070  ax6e2eq  33330

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-11 1842  ax-12 1854  ax-13 1999

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617