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Mirrors > Home > MPE Home > Th. List > ex-2nd | Structured version Visualization version GIF version |
Description: Example for df-2nd 7958. Example by David A. Wheeler. (Contributed by Mario Carneiro, 18-Jun-2015.) |
Ref | Expression |
---|---|
ex-2nd | ⊢ (2nd ‘〈3, 4〉) = 4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3ex 12276 | . 2 ⊢ 3 ∈ V | |
2 | 4re 12278 | . . 3 ⊢ 4 ∈ ℝ | |
3 | 2 | elexi 3492 | . 2 ⊢ 4 ∈ V |
4 | 1, 3 | op2nd 7966 | 1 ⊢ (2nd ‘〈3, 4〉) = 4 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1541 〈cop 4628 ‘cfv 6532 2nd c2nd 7956 ℝcr 11091 3c3 12250 4c4 12251 |
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 ax-un 7708 ax-1cn 11150 ax-icn 11151 ax-addcl 11152 ax-addrcl 11153 ax-mulcl 11154 ax-mulrcl 11155 ax-i2m1 11160 ax-1ne0 11161 ax-rrecex 11164 ax-cnre 11165 |
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-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-br 5142 df-opab 5204 df-mpt 5225 df-id 5567 df-xp 5675 df-rel 5676 df-cnv 5677 df-co 5678 df-dm 5679 df-rn 5680 df-iota 6484 df-fun 6534 df-fv 6540 df-ov 7396 df-2nd 7958 df-2 12257 df-3 12258 df-4 12259 |
This theorem is referenced by: (None) |
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