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Mirrors > Home > MPE Home > Th. List > Mathboxes > nfaov | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for operation value, analogous to nfov 7188. To prove a deduction version of this analogous to nfovd 7187 is not quickly possible because many deduction versions for bound-variable hypothesis builder for constructs the definition of alternative operation values is based on are not available (see nfafv 43342). (Contributed by Alexander van der Vekens, 26-May-2017.) |
Ref | Expression |
---|---|
nfaov.2 | ⊢ Ⅎ𝑥𝐴 |
nfaov.3 | ⊢ Ⅎ𝑥𝐹 |
nfaov.4 | ⊢ Ⅎ𝑥𝐵 |
Ref | Expression |
---|---|
nfaov | ⊢ Ⅎ𝑥 ((𝐴𝐹𝐵)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-aov 43327 | . 2 ⊢ ((𝐴𝐹𝐵)) = (𝐹'''〈𝐴, 𝐵〉) | |
2 | nfaov.3 | . . 3 ⊢ Ⅎ𝑥𝐹 | |
3 | nfaov.2 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
4 | nfaov.4 | . . . 4 ⊢ Ⅎ𝑥𝐵 | |
5 | 3, 4 | nfop 4821 | . . 3 ⊢ Ⅎ𝑥〈𝐴, 𝐵〉 |
6 | 2, 5 | nfafv 43342 | . 2 ⊢ Ⅎ𝑥(𝐹'''〈𝐴, 𝐵〉) |
7 | 1, 6 | nfcxfr 2977 | 1 ⊢ Ⅎ𝑥 ((𝐴𝐹𝐵)) |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2963 〈cop 4575 '''cafv 43323 ((caov 43324 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 ax-sep 5205 ax-nul 5212 ax-pow 5268 ax-pr 5332 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-fal 1550 df-ex 1781 df-nf 1785 df-sb 2070 df-mo 2622 df-eu 2654 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-ne 3019 df-ral 3145 df-rex 3146 df-rab 3149 df-v 3498 df-sbc 3775 df-csb 3886 df-dif 3941 df-un 3943 df-in 3945 df-ss 3954 df-nul 4294 df-if 4470 df-sn 4570 df-pr 4572 df-op 4576 df-uni 4841 df-int 4879 df-br 5069 df-opab 5131 df-id 5462 df-xp 5563 df-rel 5564 df-cnv 5565 df-co 5566 df-dm 5567 df-res 5569 df-iota 6316 df-fun 6359 df-fv 6365 df-aiota 43292 df-dfat 43325 df-afv 43326 df-aov 43327 |
This theorem is referenced by: csbaovg 43386 |
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