New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > eqeq2i | GIF version |
Description: Inference from equality to equivalence of equalities. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
eqeq2i.1 | ⊢ A = B |
Ref | Expression |
---|---|
eqeq2i | ⊢ (C = A ↔ C = B) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq2i.1 | . 2 ⊢ A = B | |
2 | eqeq2 2362 | . 2 ⊢ (A = B → (C = A ↔ C = B)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (C = A ↔ C = B) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 176 = wceq 1642 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 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: eqtri 2373 rabid2 2788 equncom 3409 ssunpr 3868 sspr 3869 sstp 3870 axprimlem2 4089 preq12b 4127 1cex 4142 dfeu2 4333 dfiota2 4340 dfnnc2 4395 addcid1 4405 addccom 4406 nnc0suc 4412 addcass 4415 nncaddccl 4419 nnsucelrlem1 4424 nndisjeq 4429 preaddccan2lem1 4454 lefinlteq 4463 ltfinex 4464 ltfintri 4466 ltlefin 4468 eqpwrelk 4478 eqtfinrelk 4486 evenodddisjlem1 4515 evenodddisj 4516 srelk 4524 dfphi2 4569 dfop2lem1 4573 dfop2 4575 dfproj12 4576 phialllem1 4616 setconslem1 4731 setconslem2 4732 dfswap2 4741 fnressn 5438 fressnfv 5439 fnov 5591 dffn5v 5706 fnov2 5707 eqerlem 5960 qsid 5990 mapexi 6003 enex 6031 elncs 6119 tcdi 6164 ovcelem1 6171 ceex 6174 nc0suc 6217 muc0or 6252 lecadd2 6266 nnc3p1n3p2 6280 nchoicelem2 6290 nchoicelem17 6305 |
Copyright terms: Public domain | W3C validator |