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Theorem fundmeng 7131
 Description: A function is equinumerous to its domain. Exercise 4 of [Suppes] p. 98. (Contributed by NM, 17-Sep-2013.)
Assertion
Ref Expression
fundmeng

Proof of Theorem fundmeng
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 funeq 5427 . . . 4
2 dmeq 5024 . . . . 5
3 id 20 . . . . 5
42, 3breq12d 4180 . . . 4
51, 4imbi12d 312 . . 3
6 vex 2916 . . . 4
76fundmen 7130 . . 3
85, 7vtoclg 2968 . 2
98imp 419 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1649   wcel 1721   class class class wbr 4167   cdm 4832   wfun 5402   cen 7056 This theorem is referenced by:  fndmeng  7133  hashf1rn  11577 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-13 1723  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2382  ax-sep 4285  ax-nul 4293  ax-pow 4332  ax-pr 4358  ax-un 4655 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2256  df-mo 2257  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2526  df-ne 2566  df-ral 2668  df-rex 2669  df-rab 2672  df-v 2915  df-sbc 3119  df-dif 3280  df-un 3282  df-in 3284  df-ss 3291  df-nul 3586  df-if 3697  df-pw 3758  df-sn 3777  df-pr 3778  df-op 3780  df-uni 3972  df-int 4007  df-br 4168  df-opab 4222  df-mpt 4223  df-id 4453  df-xp 4838  df-rel 4839  df-cnv 4840  df-co 4841  df-dm 4842  df-rn 4843  df-iota 5372  df-fun 5410  df-fn 5411  df-f 5412  df-f1 5413  df-fo 5414  df-f1o 5415  df-fv 5416  df-en 7060
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