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Metamath Proof Explorer

Theorem nfov

Description: Bound-variable hypothesis builder for operation value. (Contributed by NM, 4-May-2004)

Ref Expression
Hypotheses nfov.1 ⊢ Ⅎ _ x A
nfov.2 ⊢ Ⅎ _ x F
nfov.3 ⊢ Ⅎ _ x B
Assertion nfov ⊢ Ⅎ _ x A F B

Proof

Step Hyp Ref Expression
1 nfov.1 ⊢ Ⅎ _ x A
2 nfov.2 ⊢ Ⅎ _ x F
3 nfov.3 ⊢ Ⅎ _ x B
4 1 a1i ⊢ ⊤ → Ⅎ _ x A
5 2 a1i ⊢ ⊤ → Ⅎ _ x F
6 3 a1i ⊢ ⊤ → Ⅎ _ x B
7 4 5 6 nfovd ⊢ ⊤ → Ⅎ _ x A F B
8 7 mptru ⊢ Ⅎ _ x A F B