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Mirrors > Home > MPE Home > Th. List > jccir | Structured version Visualization version GIF version |
Description: Inference conjoining a consequent of a consequent to the right of the consequent in an implication. See also ex-natded5.3i 30157. (Contributed by Mario Carneiro, 9-Feb-2017.) (Revised by AV, 20-Aug-2019.) |
Ref | Expression |
---|---|
jccir.1 | ⊢ (𝜑 → 𝜓) |
jccir.2 | ⊢ (𝜓 → 𝜒) |
Ref | Expression |
---|---|
jccir | ⊢ (𝜑 → (𝜓 ∧ 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | jccir.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | jccir.2 | . . 3 ⊢ (𝜓 → 𝜒) | |
3 | 1, 2 | syl 17 | . 2 ⊢ (𝜑 → 𝜒) |
4 | 1, 3 | jca 511 | 1 ⊢ (𝜑 → (𝜓 ∧ 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-an 396 |
This theorem is referenced by: jccil 522 oelim2 8591 maxprmfct 16649 chpmat1dlem 22681 chpdmatlem2 22685 leordtvallem1 23058 leordtvallem2 23059 mbfmax 25522 wlklnwwlkln2lem 29631 0wlkonlem1 29866 2cycl2d 34648 relowlpssretop 36746 ntrclsk13 43372 smonoord 46585 |
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