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Mirrors > Home > NFE Home > Th. List > syl6reqr | GIF version |
Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998.) |
Ref | Expression |
---|---|
syl6reqr.1 | ⊢ (φ → A = B) |
syl6reqr.2 | ⊢ C = B |
Ref | Expression |
---|---|
syl6reqr | ⊢ (φ → C = A) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl6reqr.1 | . 2 ⊢ (φ → A = B) | |
2 | syl6reqr.2 | . . 3 ⊢ C = B | |
3 | 2 | eqcomi 2357 | . 2 ⊢ B = C |
4 | 1, 3 | syl6req 2402 | 1 ⊢ (φ → C = A) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1642 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-ex 1542 df-cleq 2346 |
This theorem is referenced by: iftrue 3668 iffalse 3669 difprsn1 3847 funimacnv 5168 dfimafn 5366 fniinfv 5372 fvco2 5382 fniunfv 5466 isoini 5497 dmmptg 5684 nchoicelem14 6302 |
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