New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > iotabii | GIF version |
Description: Formula-building deduction rule for iota. (Contributed by Mario Carneiro, 2-Oct-2015.) |
Ref | Expression |
---|---|
iotabii.1 | ⊢ (φ ↔ ψ) |
Ref | Expression |
---|---|
iotabii | ⊢ (℩xφ) = (℩xψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iotabi 4348 | . 2 ⊢ (∀x(φ ↔ ψ) → (℩xφ) = (℩xψ)) | |
2 | iotabii.1 | . 2 ⊢ (φ ↔ ψ) | |
3 | 1, 2 | mpg 1548 | 1 ⊢ (℩xφ) = (℩xψ) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 176 = wceq 1642 ℩cio 4337 |
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-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rex 2620 df-uni 3892 df-iota 4339 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |