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Mirrors > Home > NFE Home > Th. List > aecoms | GIF version |
Description: A commutation rule for identical variable specifiers. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
alequcoms.1 | ⊢ (∀x x = y → φ) |
Ref | Expression |
---|---|
aecoms | ⊢ (∀y y = x → φ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aecom 1946 | . 2 ⊢ (∀y y = x → ∀x x = y) | |
2 | alequcoms.1 | . 2 ⊢ (∀x x = y → φ) | |
3 | 1, 2 | syl 15 | 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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 |
This theorem is referenced by: hbae 1953 dvelimh 1964 dral1 1965 |
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