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Mirrors > Home > ILE Home > Th. List > pm3.21 | GIF version |
Description: Join antecedents with conjunction. Theorem *3.21 of [WhiteheadRussell] p. 111. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
pm3.21 | ⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜑))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.2 126 | . 2 ⊢ (𝜓 → (𝜑 → (𝜓 ∧ 𝜑))) | |
2 | 1 | com12 27 | 1 ⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜑))) |
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: pm3.22 252 iba 284 ancr 304 anc2r 311 pm5.31 330 xoranor 1268 19.41h 1575 19.41 1576 ltsopr 6694 bj-findis 10104 |
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