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Mirrors > Home > MPE Home > Th. List > Mathboxes > int-eqtransd | Structured version Visualization version GIF version |
Description: EqualityTransitivity generator rule. (Contributed by Stanislas Polu, 7-Apr-2020.) |
Ref | Expression |
---|---|
int-eqtransd.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
int-eqtransd.2 | ⊢ (𝜑 → 𝐵 = 𝐶) |
Ref | Expression |
---|---|
int-eqtransd | ⊢ (𝜑 → 𝐴 = 𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | int-eqtransd.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
2 | int-eqtransd.2 | . 2 ⊢ (𝜑 → 𝐵 = 𝐶) | |
3 | 1, 2 | eqtrd 2856 | 1 ⊢ (𝜑 → 𝐴 = 𝐶) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1533 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-9 2120 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1777 df-cleq 2814 |
This theorem is referenced by: (None) |
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