Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nfeq2 | GIF version |
Description: Hypothesis builder for equality, special case. (Contributed by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
nfeq2.1 | ⊢ Ⅎ𝑥𝐵 |
Ref | Expression |
---|---|
nfeq2 | ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2299 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | nfeq2.1 | . 2 ⊢ Ⅎ𝑥𝐵 | |
3 | 1, 2 | nfeq 2307 | 1 ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
Colors of variables: wff set class |
Syntax hints: = wceq 1335 Ⅎwnf 1440 Ⅎwnfc 2286 |
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-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-cleq 2150 df-clel 2153 df-nfc 2288 |
This theorem is referenced by: issetf 2719 eqvincf 2837 csbhypf 3069 nfpr 3609 intab 3836 nfmpt 4056 cbvmptf 4058 cbvmpt 4059 repizf2 4123 moop2 4211 eusvnf 4413 elrnmpt1 4837 fmptco 5633 elabrex 5708 nfmpo 5890 cbvmpox 5899 ovmpodxf 5946 fmpox 6148 f1od2 6182 nfrecs 6254 erovlem 6572 xpf1o 6789 mapxpen 6793 mkvprop 7101 cc3 7188 lble 8818 nfsum1 11253 nfsum 11254 zsumdc 11281 fsum3 11284 fsum3cvg2 11291 fsum2dlemstep 11331 mertenslem2 11433 nfcprod1 11451 nfcprod 11452 zproddc 11476 fprod2dlemstep 11519 ctiunctlemfo 12168 ellimc3apf 13029 |
Copyright terms: Public domain | W3C validator |