Theorem funmo 2680

Description: A function has at most one value for each argument.

Assertion

Ref	Expression
funmo	⊢ (Fun A → ∃*y xAy)

Distinct variable group(s):   x,y,A

Proof of Theorem funmo

Step	Hyp	Ref	Expression
1		dffunmo 2679	. . 3 ⊢ (Fun A ↔ (Rel A ∧ ∀x∃*y xAy))
2	1	pm3.27bd 263	. 2 ⊢ (Fun A → ∀x∃*y xAy)
3	2	19.21bi 742	1 ⊢ (Fun A → ∃*y xAy)

Syntax hints:   → wi 2  ∀wal 672  ∃*wmo 1008   class class class wbr 2054  Rel wrel 2415  Fun wfun 2416

This theorem is referenced by:  funco 2696  imadif 2714

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-13 804  ax-14 805  ax-16 922  ax-17 925  ax-ext 1074  ax-rep 1075  ax-pow 1077

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-eu 1009  df-mo 1010  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-dif 1489  df-un 1490  df-in 1491  df-ss 1492  df-nul 1708  df-pw 1799  df-sn 1811  df-pr 1812  df-op 1815  df-br 2063  df-opab 2098  df-id 2125  df-cnv 2426  df-co 2427  df-fun 2432

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