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Mirrors > Home > MPE Home > Th. List > ofeq | Structured version Visualization version GIF version |
Description: Equality theorem for function operation. (Contributed by Mario Carneiro, 20-Jul-2014.) |
Ref | Expression |
---|---|
ofeq | ⊢ (𝑅 = 𝑆 → ∘f 𝑅 = ∘f 𝑆) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . 2 ⊢ (𝑅 = 𝑆 → 𝑅 = 𝑆) | |
2 | 1 | ofeqd 7684 | 1 ⊢ (𝑅 = 𝑆 → ∘f 𝑅 = ∘f 𝑆) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1534 ∘f cof 7680 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2697 |
This theorem depends on definitions: df-bi 206 df-an 395 df-3an 1086 df-tru 1537 df-ex 1775 df-sb 2061 df-clab 2704 df-cleq 2718 df-clel 2803 df-v 3464 df-ss 3963 df-uni 4906 df-br 5146 df-opab 5208 df-mpt 5229 df-iota 6498 df-fv 6554 df-ov 7419 df-oprab 7420 df-mpo 7421 df-of 7682 |
This theorem is referenced by: resspsrvsca 21982 sitmval 34196 mhphf2 42288 mendplusgfval 42883 mendvscafval 42888 |
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