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Mirrors > Home > ILE Home > Th. List > jctir | GIF version |
Description: Inference conjoining a theorem to right of consequent in an implication. (Contributed by NM, 31-Dec-1993.) |
Ref | Expression |
---|---|
jctil.1 | ⊢ (𝜑 → 𝜓) |
jctil.2 | ⊢ 𝜒 |
Ref | Expression |
---|---|
jctir | ⊢ (𝜑 → (𝜓 ∧ 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | jctil.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | jctil.2 | . . 3 ⊢ 𝜒 | |
3 | 2 | a1i 9 | . 2 ⊢ (𝜑 → 𝜒) |
4 | 1, 3 | jca 290 | 1 ⊢ (𝜑 → (𝜓 ∧ 𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia3 101 |
This theorem is referenced by: jctr 298 equvini 1641 funtp 4952 foimacnv 5144 respreima 5295 fpr 5345 dmtpos 5871 ssdomg 6258 archnqq 6515 recexgt0sr 6858 ige2m2fzo 9054 climeu 9817 algcvgblem 9888 |
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