Theorem ax12b 2086

Description: A bidirectional version of axc15 2085. (Contributed by NM, 30-Jun-2006.)

Assertion

Ref	Expression
ax12b

Proof of Theorem ax12b

Step	Hyp	Ref	Expression
1		axc15 2085	. . 3
2	1	imp 429	. 2
3		sp 1859	. . . 4
4	3	com12 31	. . 3
5	4	adantl 466	. 2
6	2, 5	impbid 191	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393

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  ax-13 1999

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