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Theorem cmpida 25877
 Description: The 10th "axiom" of a category: is a left neutral element. (Contributed by FL, 29-Oct-2007.)
Hypotheses
Ref Expression
cmpida.1
cmpida.2
cmpida.3
cmpida.4
cmpida.5
cmpida.6
Assertion
Ref Expression
cmpida

Proof of Theorem cmpida
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 cmpida.2 . . . 4
2 cmpida.6 . . . 4
3 cmpida.4 . . . 4
4 cmpida.5 . . . 4
5 cmpida.1 . . . 4
6 cmpida.3 . . . 4
71, 2, 3, 4, 5, 6cati 25858 . . 3
8 eqeq2 2305 . . . . . . 7
9 fveq2 5541 . . . . . . . . 9
109oveq1d 5889 . . . . . . . 8
1110eqeq1d 2304 . . . . . . 7
128, 11imbi12d 311 . . . . . 6
13 fveq2 5541 . . . . . . . 8
1413eqeq1d 2304 . . . . . . 7
15 oveq2 5882 . . . . . . . 8
16 id 19 . . . . . . . 8
1715, 16eqeq12d 2310 . . . . . . 7
1814, 17imbi12d 311 . . . . . 6
1912, 18rspc2v 2903 . . . . 5
2019com12 27 . . . 4