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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > aecoms-o | Structured version Visualization version GIF version |
Description: A commutation rule for identical variable specifiers. Version of aecoms 2393 using ax-c11 35035. (Contributed by NM, 10-May-1993.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
alequcoms-o.1 | ⊢ (∀𝑥 𝑥 = 𝑦 → 𝜑) |
Ref | Expression |
---|---|
aecoms-o | ⊢ (∀𝑦 𝑦 = 𝑥 → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aecom-o 35049 | . 2 ⊢ (∀𝑦 𝑦 = 𝑥 → ∀𝑥 𝑥 = 𝑦) | |
2 | alequcoms-o.1 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → 𝜑) | |
3 | 1, 2 | syl 17 | 1 ⊢ (∀𝑦 𝑦 = 𝑥 → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1599 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2054 ax-c5 35031 ax-c4 35032 ax-c7 35033 ax-c10 35034 ax-c11 35035 ax-c9 35038 |
This theorem depends on definitions: df-bi 199 df-an 387 df-ex 1824 |
This theorem is referenced by: hbae-o 35051 dral1-o 35052 dvelimf-o 35077 aev-o 35079 ax12indalem 35093 ax12inda2ALT 35094 |
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