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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 2201 | . 2 ⊢ 𝐴 = 𝐶 |
4 | 3eqtr2i.3 | . 2 ⊢ 𝐶 = 𝐷 | |
5 | 3, 4 | eqtri 2198 | 1 ⊢ 𝐴 = 𝐷 |
Colors of variables: wff set class |
Syntax hints: = wceq 1353 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-gen 1449 ax-4 1510 ax-17 1526 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-cleq 2170 |
This theorem is referenced by: dfrab3 3411 iunid 3941 cnvcnv 5080 cocnvcnv2 5139 fmptap 5705 exmidfodomrlemim 7197 negdii 8237 halfpm6th 9135 numma 9423 numaddc 9427 6p5lem 9449 8p2e10 9459 binom2i 10623 0.999... 11522 flodddiv4 11931 6gcd4e2 11988 dfphi2 12212 txswaphmeolem 13691 cosq23lt0 14125 pigt3 14136 nninfomni 14628 |
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