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Mirrors > Home > ILE Home > Th. List > anim12ci | GIF version |
Description: Variant of anim12i 338 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
Ref | Expression |
---|---|
anim12i.1 | ⊢ (𝜑 → 𝜓) |
anim12i.2 | ⊢ (𝜒 → 𝜃) |
Ref | Expression |
---|---|
anim12ci | ⊢ ((𝜑 ∧ 𝜒) → (𝜃 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anim12i.2 | . . 3 ⊢ (𝜒 → 𝜃) | |
2 | anim12i.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
3 | 1, 2 | anim12i 338 | . 2 ⊢ ((𝜒 ∧ 𝜑) → (𝜃 ∧ 𝜓)) |
4 | 3 | ancoms 268 | 1 ⊢ ((𝜑 ∧ 𝜒) → (𝜃 ∧ 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem is referenced by: anim1ci 341 dfco2a 5125 funco 5252 fliftval 5795 ltsrprg 7734 difelfznle 10118 iseqf1olemqk 10477 difsqpwdvds 12317 mhmco 12761 ex-ceil 14127 |
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