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Metamath Proof Explorer

Theorem symgfv

Description: The function value of a permutation. (Contributed by AV, 1-Jan-2019)

Ref Expression
Hypotheses symgbas.1 ⊢ G = SymGrp ⁡ A
symgbas.2 ⊢ B = Base G
Assertion symgfv ⊢ F ∈ B ∧ X ∈ A → F ⁡ X ∈ A

Proof

Step Hyp Ref Expression
1 symgbas.1 ⊢ G = SymGrp ⁡ A
2 symgbas.2 ⊢ B = Base G
3 1 2 symgbasf ⊢ F ∈ B → F : A ⟶ A
4 3 ffvelcdmda ⊢ F ∈ B ∧ X ∈ A → F ⁡ X ∈ A