![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
Mirrors > Home > MPE Home > Th. List > equidq | Structured version Unicode version |
Description: equid 1731 with universal quantifier without using ax-c5 2194 or ax-5 1671. (Contributed by NM, 13-Jan-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
equidq |
![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equidqe 2232 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | ax10 2206 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | hbequid 2219 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 3 | con3i 135 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 2, 4 | alrimih 1613 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | 1, 5 | mt3 180 |
1
![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-7 1730 ax-c5 2194 ax-c4 2195 ax-c7 2196 ax-c10 2197 ax-c9 2201 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |