Mathbox for Norm Megill |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > aecom-o | Structured version Visualization version Unicode version |
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 2311 using ax-c11 34172. Unlike axc11nfromc11 34211, this version does not require ax-5 1839 (see comment of equcomi1 34185). (Contributed by NM, 10-May-1993.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
aecom-o |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-c11 34172 | . . 3 | |
2 | 1 | pm2.43i 52 | . 2 |
3 | equcomi1 34185 | . . 3 | |
4 | 3 | alimi 1739 | . 2 |
5 | 2, 4 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wal 1481 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-c5 34168 ax-c4 34169 ax-c7 34170 ax-c10 34171 ax-c11 34172 ax-c9 34175 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 |
This theorem is referenced by: aecoms-o 34187 naecoms-o 34212 aev-o 34216 ax12indalem 34230 |
Copyright terms: Public domain | W3C validator |