Theorem aecom-o 2230

Description: Commutation law for identical variable specifiers. The antecedent and consequent are true when and are substituted with the same variable. Lemma L12 in [Megill] p. 445 (p. 12 of the preprint). Version of aecom 2051 using ax-c11 2218. Unlike axc11nfromc11 2256, this version does not require ax-5 1704. (Contributed by NM, 10-May-1993.) (New usage is discouraged.)

Assertion

Ref	Expression
aecom-o

Proof of Theorem aecom-o

Step	Hyp	Ref	Expression
1		ax-c11 2218	. . 3
2	1	pm2.43i 47	. 2
3		equcomi 1793	. . 3
4	3	alimi 1633	. 2
5	2, 4	syl 16	1

Syntax hints:  ->wi 4  A.wal 1393

This theorem is referenced by:  aecoms-o  2231  naecoms-o  2257  aev-o  2261  ax12indalem  2275

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-c11 2218

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