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Mirrors > Home > ILE Home > Th. List > alequcoms | 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 |
---|---|
alequcoms | ⊢ (∀𝑦 𝑦 = 𝑥 → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alequcom 1408 | . 2 ⊢ (∀𝑦 𝑦 = 𝑥 → ∀𝑥 𝑥 = 𝑦) | |
2 | alequcoms.1 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → 𝜑) | |
3 | 1, 2 | syl 14 | 1 ⊢ (∀𝑦 𝑦 = 𝑥 → 𝜑) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1241 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-10 1396 |
This theorem is referenced by: hbae 1606 dral1 1618 drex1 1679 aev 1693 sbequi 1720 |
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