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Mirrors > Home > ILE Home > Th. List > 3eqtr2i | GIF version |
Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006.) |
Ref | Expression |
---|---|
3eqtr2i.1 | ⊢ 𝐴 = 𝐵 |
3eqtr2i.2 | ⊢ 𝐶 = 𝐵 |
3eqtr2i.3 | ⊢ 𝐶 = 𝐷 |
Ref | Expression |
---|---|
3eqtr2i | ⊢ 𝐴 = 𝐷 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3eqtr2i.1 | . . 3 ⊢ 𝐴 = 𝐵 | |
2 | 3eqtr2i.2 | . . 3 ⊢ 𝐶 = 𝐵 | |
3 | 1, 2 | eqtr4i 2161 | . 2 ⊢ 𝐴 = 𝐶 |
4 | 3eqtr2i.3 | . 2 ⊢ 𝐶 = 𝐷 | |
5 | 3, 4 | eqtri 2158 | 1 ⊢ 𝐴 = 𝐷 |
Colors of variables: wff set class |
Syntax hints: = wceq 1331 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-gen 1425 ax-4 1487 ax-17 1506 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-cleq 2130 |
This theorem is referenced by: dfrab3 3347 iunid 3863 cnvcnv 4986 cocnvcnv2 5045 fmptap 5603 exmidfodomrlemim 7050 negdii 8039 halfpm6th 8933 numma 9218 numaddc 9222 6p5lem 9244 8p2e10 9254 binom2i 10394 0.999... 11283 flodddiv4 11620 6gcd4e2 11672 dfphi2 11885 txswaphmeolem 12478 cosq23lt0 12903 pigt3 12914 nninfomni 13204 |
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