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Theorem cmpidb 25878
 Description: The 11th "axiom" of a category: is a right neutral element. (Contributed by FL, 24-Oct-2007.)
Hypotheses
Ref Expression
cmpidb.1
cmpidb.2
cmpidb.3
cmpidb.4
cmpidb.5
Assertion
Ref Expression
cmpidb

Proof of Theorem cmpidb
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 cmpidb.2 . . . 4
2 eqid 2296 . . . 4
3 cmpidb.4 . . . 4
4 cmpidb.5 . . . 4
5 cmpidb.1 . . . 4
6 cmpidb.3 . . . 4
71, 2, 3, 4, 5, 6cati 25858 . . 3
8 eqeq2 2305 . . . . . . 7
9 fveq2 5541 . . . . . . . . 9
109oveq2d 5890 . . . . . . . 8
1110eqeq1d 2304 . . . . . . 7
128, 11imbi12d 311 . . . . . 6
13 fveq2 5541 . . . . . . . 8
1413eqeq1d 2304 . . . . . . 7
15 oveq1 5881 . . . . . . . 8
16 id 19 . . . . . . . 8
1715, 16eqeq12d 2310 . . . . . . 7
1814, 17imbi12d 311 . . . . . 6
1912, 18rspc2v 2903 . . . . 5
2019com12 27 . . . 4