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Mathbox for Alexander van der Vekens |
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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 7423. To prove a deduction version of this analogous to nfovd 7422 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 45614). (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 45599 | . 2 ⊢ ((𝐴𝐹𝐵)) = (𝐹'''〈𝐴, 𝐵〉) | |
2 | nfaov.3 | . . 3 ⊢ Ⅎ𝑥𝐹 | |
3 | nfaov.2 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
4 | nfaov.4 | . . . 4 ⊢ Ⅎ𝑥𝐵 | |
5 | 3, 4 | nfop 4882 | . . 3 ⊢ Ⅎ𝑥〈𝐴, 𝐵〉 |
6 | 2, 5 | nfafv 45614 | . 2 ⊢ Ⅎ𝑥(𝐹'''〈𝐴, 𝐵〉) |
7 | 1, 6 | nfcxfr 2900 | 1 ⊢ Ⅎ𝑥 ((𝐴𝐹𝐵)) |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2882 〈cop 4628 '''cafv 45595 ((caov 45596 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2702 ax-sep 5292 ax-nul 5299 ax-pr 5420 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2533 df-eu 2562 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-ne 2940 df-ral 3061 df-rex 3070 df-rab 3432 df-v 3475 df-sbc 3774 df-csb 3890 df-dif 3947 df-un 3949 df-in 3951 df-ss 3961 df-nul 4319 df-if 4523 df-sn 4623 df-pr 4625 df-op 4629 df-uni 4902 df-int 4944 df-br 5142 df-opab 5204 df-id 5567 df-xp 5675 df-rel 5676 df-cnv 5677 df-co 5678 df-dm 5679 df-res 5681 df-iota 6484 df-fun 6534 df-fv 6540 df-aiota 45563 df-dfat 45597 df-afv 45598 df-aov 45599 |
This theorem is referenced by: csbaovg 45658 |
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