Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > mp1i | GIF version |
Description: Drop and replace an antecedent. (Contributed by Stefan O'Rear, 29-Jan-2015.) |
Ref | Expression |
---|---|
mp1i.a | ⊢ 𝜑 |
mp1i.b | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
mp1i | ⊢ (𝜒 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mp1i.a | . . 3 ⊢ 𝜑 | |
2 | mp1i.b | . . 3 ⊢ (𝜑 → 𝜓) | |
3 | 1, 2 | ax-mp 7 | . 2 ⊢ 𝜓 |
4 | 3 | a1i 9 | 1 ⊢ (𝜒 → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-1 5 ax-mp 7 |
This theorem is referenced by: poirr2 4717 relcoi2 4848 tfrlemi14d 5947 findcard2d 6348 findcard2sd 6349 ac6sfi 6352 cauappcvgprlemladd 6756 caucvgprprlemmu 6793 caucvgsrlemfv 6875 recidpirqlemcalc 6933 recidpirq 6934 |
Copyright terms: Public domain | W3C validator |