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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 2428 using ax-c11 36544. (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 36558 | . 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 1540 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-c5 36540 ax-c4 36541 ax-c7 36542 ax-c10 36543 ax-c11 36544 ax-c9 36547 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1787 |
This theorem is referenced by: hbae-o 36560 dral1-o 36561 dvelimf-o 36586 aev-o 36588 ax12indalem 36602 ax12inda2ALT 36603 |
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