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| Description: A commutation rule for identical variable specifiers. Usage of this theorem is discouraged because it depends on ax-13 2377. (Contributed by NM, 10-May-1993.) (New usage is discouraged.) | 
| Ref | Expression | 
|---|---|
| aecoms.1 | ⊢ (∀𝑥 𝑥 = 𝑦 → 𝜑) | 
| Ref | Expression | 
|---|---|
| aecoms | ⊢ (∀𝑦 𝑦 = 𝑥 → 𝜑) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | aecom 2432 | . 2 ⊢ (∀𝑦 𝑦 = 𝑥 ↔ ∀𝑥 𝑥 = 𝑦) | |
| 2 | aecoms.1 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → 𝜑) | |
| 3 | 1, 2 | sylbi 217 | 1 ⊢ (∀𝑦 𝑦 = 𝑥 → 𝜑) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∀wal 1538 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-10 2141 ax-12 2177 ax-13 2377 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-nf 1784 | 
| This theorem is referenced by: axc11 2435 nd4 10630 axrepnd 10634 axpownd 10641 axregnd 10644 axinfnd 10646 axacndlem5 10651 axacnd 10652 wl-ax11-lem1 37586 wl-ax11-lem3 37588 wl-ax11-lem9 37594 wl-ax11-lem10 37595 e2ebind 44583 | 
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